Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind type parameter. More...

Detailed Description

Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind type parameter.

See the documentation of setFFTR for more details.

Parameters

[in]

data

: The input contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.

Returns: fft : The output vector of the same type, kind, and size as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftpack, only: getFFTR

fft = getFFTR(data(:))

pm_fftpack::getFFTR
Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type compl...
Definition: pm_fftpack.F90:1156

pm_fftpack
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftpack.F90:205

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTR.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftpack, only: getfactorFFT

6 use pm_fftpack, only: getFFTF, getFFTR

7 use pm_distUnif, only: getUnifRand

8 use pm_mathCompare, only: isClose

9 use pm_err, only: setAsserted

10

11 implicit none

12

13 integer(IK) :: i

14 integer(IK) :: lenData

15 type(display_type) :: disp

16 disp = display_type(file = "main.out.F90")

17

18 do i = 1, 5

19 block

20 use pm_kind, only: TKG => CKS

21 real(TKG) :: reltol

22 complex(TKG), allocatable :: data(:), adat(:)

23 call disp%show("lenData = getUnifRand(5, 100)")

24 lenData = getUnifRand(5, 100)

25 call disp%show("lenData")

26 call disp%show( lenData )

27 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

28 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

29 call disp%show("data")

30 call disp%show( data )

31 call disp%skip()

32 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

33 adat = getFFTR(getFFTF(data)) / size(data)

34 call disp%show("adat")

35 call disp%show( adat )

36 call disp%show("reltol = sqrt(epsilon(1._TKG))")

37 reltol = sqrt(epsilon(1._TKG))

38 call disp%show("reltol")

39 call disp%show( reltol )

40 call disp%show("isClose(data, adat, reltol = reltol)")

41 call disp%show( isClose(data, adat, reltol = reltol) )

42 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

43 call setAsserted(all(isClose(data, adat, reltol = reltol)))

44 call disp%skip()

45 end block

46

47 block

48 use pm_kind, only: TKG => CKD

49 real(TKG) :: reltol

50 complex(TKG), allocatable :: data(:), adat(:)

51 call disp%show("lenData = getUnifRand(5, 100)")

52 lenData = getUnifRand(5, 100)

53 call disp%show("lenData")

54 call disp%show( lenData )

55 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

56 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

57 call disp%show("data")

58 call disp%show( data )

59 call disp%skip()

60 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

61 adat = getFFTR(getFFTF(data)) / size(data)

62 call disp%show("adat")

63 call disp%show( adat )

64 call disp%show("reltol = sqrt(epsilon(1._TKG))")

65 reltol = sqrt(epsilon(1._TKG))

66 call disp%show("reltol")

67 call disp%show( reltol )

68 call disp%show("isClose(data, adat, reltol = reltol)")

69 call disp%show( isClose(data, adat, reltol = reltol) )

70 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

71 call setAsserted(all(isClose(data, adat, reltol = reltol)))

72 call disp%skip()

73 end block

74

75 block

76 use pm_kind, only: TKG => CKH

77 real(TKG) :: reltol

78 complex(TKG), allocatable :: data(:), adat(:)

79 call disp%show("lenData = getUnifRand(5, 100)")

80 lenData = getUnifRand(5, 100)

81 call disp%show("lenData")

82 call disp%show( lenData )

83 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

84 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

85 call disp%show("data")

86 call disp%show( data )

87 call disp%skip()

88 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

89 adat = getFFTR(getFFTF(data)) / size(data)

90 call disp%show("adat")

91 call disp%show( adat )

92 call disp%show("reltol = sqrt(epsilon(1._TKG))")

93 reltol = sqrt(epsilon(1._TKG))

94 call disp%show("reltol")

95 call disp%show( reltol )

96 call disp%show("isClose(data, adat, reltol = reltol)")

97 call disp%show( isClose(data, adat, reltol = reltol) )

98 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

99 call setAsserted(all(isClose(data, adat, reltol = reltol)))

100 call disp%skip()

101 end block

102

103 block

104 use pm_kind, only: TKG => RKS

105 real(TKG) :: reltol

106 real(TKG), allocatable :: data(:), adat(:)

107 call disp%show("lenData = getUnifRand(5, 100)")

108 lenData = getUnifRand(5, 100)

109 call disp%show("lenData")

110 call disp%show( lenData )

111 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

112 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

113 call disp%show("data")

114 call disp%show( data )

115 call disp%skip()

116 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

117 adat = getFFTR(getFFTF(data)) / size(data)

118 call disp%show("adat")

119 call disp%show( adat )

120 call disp%show("reltol = sqrt(epsilon(1._TKG))")

121 reltol = sqrt(epsilon(1._TKG))

122 call disp%show("reltol")

123 call disp%show( reltol )

124 call disp%show("isClose(data, adat, reltol = reltol)")

125 call disp%show( isClose(data, adat, reltol = reltol) )

126 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

127 call setAsserted(all(isClose(data, adat, reltol = reltol)))

128 call disp%skip()

129 end block

130

131 block

132 use pm_kind, only: TKG => RKD

133 real(TKG) :: reltol

134 real(TKG), allocatable :: data(:), adat(:)

135 call disp%show("lenData = getUnifRand(5, 100)")

136 lenData = getUnifRand(5, 100)

137 call disp%show("lenData")

138 call disp%show( lenData )

139 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

140 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

141 call disp%show("data")

142 call disp%show( data )

143 call disp%skip()

144 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

145 adat = getFFTR(getFFTF(data)) / size(data)

146 call disp%show("adat")

147 call disp%show( adat )

148 call disp%show("reltol = sqrt(epsilon(1._TKG))")

149 reltol = sqrt(epsilon(1._TKG))

150 call disp%show("reltol")

151 call disp%show( reltol )

152 call disp%show("isClose(data, adat, reltol = reltol)")

153 call disp%show( isClose(data, adat, reltol = reltol) )

154 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

155 call setAsserted(all(isClose(data, adat, reltol = reltol)))

156 call disp%skip()

157 end block

158

159 block

160 use pm_kind, only: TKG => RKH

161 real(TKG) :: reltol

162 real(TKG), allocatable :: data(:), adat(:)

163 call disp%show("lenData = getUnifRand(5, 100)")

164 lenData = getUnifRand(5, 100)

165 call disp%show("lenData")

166 call disp%show( lenData )

167 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

168 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

169 call disp%show("data")

170 call disp%show( data )

171 call disp%skip()

172 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

173 adat = getFFTR(getFFTF(data)) / size(data)

174 call disp%show("adat")

175 call disp%show( adat )

176 call disp%show("reltol = sqrt(epsilon(1._TKG))")

177 reltol = sqrt(epsilon(1._TKG))

178 call disp%show("reltol")

179 call disp%show( reltol )

180 call disp%show("isClose(data, adat, reltol = reltol)")

181 call disp%show( isClose(data, adat, reltol = reltol) )

182 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

183 call setAsserted(all(isClose(data, adat, reltol = reltol)))

184 call disp%skip()

185 end block

186 end do

187

188end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

pm_fftpack::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftpack.F90:746

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:535

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:843

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:570

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:571

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)

2lenData

3+100

4data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

5data

6(+1.95767736, +0.340019941), (+1.69411159, +0.184722662), (+1.99609685, +0.874795973), (+1.23013997, +0.268832743), (+1.70646000, +0.848967195), (+1.98596430, +0.825376511E-1), (+1.98011351, +0.216663480E-1), (+1.14775097, +0.458009124), (+1.27637529, +0.737147331E-1), (+1.75623941, +0.121651888), (+1.73738432, +0.768683910), (+1.38725305, +0.456090808), (+1.63624310, +0.221452236), (+1.65104115, +0.678625941), (+1.44143033, +0.164538145), (+1.64939535, +0.993191898), (+1.38695145, +0.558130682), (+1.09806275, +0.474977493E-1), (+1.50789690, +0.714100122), (+1.47923136, +0.627494574), (+1.16684222, +0.393144250), (+1.02994585, +0.905567884), (+1.21860123, +0.746505499), (+1.25337899, +0.541254997), (+1.18987775, +0.302046061), (+1.54788566, +0.398060799), (+1.45420551, +0.667210102), (+1.31424665, +0.649591923), (+1.44759870, +0.765276074), (+1.53104389, +0.491430759E-1), (+1.28021169, +0.838705957), (+1.51285195, +0.856796384), (+1.07026172, +0.828471839), (+1.20042038, +0.687558651E-1), (+1.58710885, +0.827026069), (+1.33087707, +0.454344749), (+1.49962509, +0.835164011), (+1.71184587, +0.307528138), (+1.32429183, +0.727030575), (+1.85422194, +0.567117929), (+1.79878676, +0.852418840), (+1.62232113, +0.107852578), (+1.80184519, +0.312124074), (+1.23287201, +0.885697544), (+1.69501972, +0.386821687), (+1.93323052, +0.176185966), (+1.87080657, +0.971192658), (+1.03978992, +0.232512653), (+1.84335887, +0.588546336), (+1.59750307, +0.944916606), (+1.04299879, +0.153619587), (+1.90495539, +0.625362098), (+1.23835468, +0.690837502), (+1.01438522, +0.169849873), (+1.72351170, +0.694569826), (+1.15620708, +0.703267694), (+1.07901800, +0.510550559), (+1.03597987, +0.318468094), (+1.70964694, +0.280686259), (+1.44137001, +0.792760432), (+1.32566237, +0.992996991), (+1.03721368, +0.483505070), (+1.53323543, +0.254247069), (+1.53515589, +0.430958867), (+1.17242169, +0.408739328), (+1.56498992, +0.925855219), (+1.61202335, +0.691056848), (+1.42595756, +0.782053769), (+1.59482646, +0.792135537), (+1.77879620, +0.512541652), (+1.50887489, +0.577588379), (+1.60343909, +0.988416374), (+1.18402827, +0.382843077), (+1.10620070, +0.800054908), (+1.26737678, +0.585495770), (+1.46787858, +0.501343906), (+1.68477249, +0.274804890), (+1.32004082, +0.999499321), (+1.63934493, +0.137591481), (+1.93228436, +0.785169184), (+1.50438857, +0.385290980), (+1.72426701, +0.150979996), (+1.95007873, +0.426890850), (+1.44123876, +0.967406332), (+1.52670038, +0.999591589), (+1.92924917, +0.464909017), (+1.66190171, +0.203791320), (+1.84291470, +0.168471813), (+1.39692998, +0.816338301), (+1.84116697, +0.442754030E-1), (+1.42866027, +0.229278803), (+1.70166779, +0.148472786E-1), (+1.03814340, +0.315181434), (+1.05549455, +0.164465606), (+1.37814212, +0.288693726), (+1.56994700, +0.899730086), (+1.23159552, +0.842171729), (+1.21974945, +0.673607051), (+1.20658779, +0.624697149), (+1.82479978, +0.675698817)

7

8adat = getFFTR(getFFTF(data)) / size(data)

9adat

10(+1.95767689, +0.340019822), (+1.69411099, +0.184722602), (+1.99609697, +0.874795914), (+1.23013973, +0.268832743), (+1.70645976, +0.848967195), (+1.98596418, +0.825375393E-1), (+1.98011363, +0.216663741E-1), (+1.14775109, +0.458009034), (+1.27637553, +0.737146959E-1), (+1.75623906, +0.121651880), (+1.73738384, +0.768683910), (+1.38725317, +0.456090748), (+1.63624334, +0.221452296), (+1.65104127, +0.678626120), (+1.44143069, +0.164538130), (+1.64939499, +0.993191898), (+1.38695133, +0.558130741), (+1.09806275, +0.474977307E-1), (+1.50789738, +0.714100122), (+1.47923136, +0.627494633), (+1.16684210, +0.393144161), (+1.02994585, +0.905567944), (+1.21860135, +0.746505380), (+1.25337899, +0.541255116), (+1.18987763, +0.302046269), (+1.54788530, +0.398060530), (+1.45420516, +0.667209983), (+1.31424654, +0.649591804), (+1.44759870, +0.765276015), (+1.53104341, +0.491430573E-1), (+1.28021145, +0.838705897), (+1.51285207, +0.856796324), (+1.07026172, +0.828471899), (+1.20042050, +0.687558651E-1), (+1.58710897, +0.827026367), (+1.33087683, +0.454344720), (+1.49962497, +0.835164011), (+1.71184587, +0.307528228), (+1.32429230, +0.727030694), (+1.85422182, +0.567117929), (+1.79878664, +0.852418840), (+1.62232089, +0.107852571), (+1.80184543, +0.312124014), (+1.23287213, +0.885697603), (+1.69501972, +0.386821747), (+1.93323040, +0.176185757), (+1.87080669, +0.971192718), (+1.03978992, +0.232512549), (+1.84335923, +0.588546276), (+1.59750295, +0.944916666), (+1.04299831, +0.153619334), (+1.90495479, +0.625361979), (+1.23835468, +0.690837562), (+1.01438487, +0.169849753), (+1.72351146, +0.694569945), (+1.15620708, +0.703267515), (+1.07901800, +0.510550678), (+1.03597987, +0.318467945), (+1.70964742, +0.280686378), (+1.44136977, +0.792760491), (+1.32566190, +0.992996991), (+1.03721333, +0.483505100), (+1.53323543, +0.254247099), (+1.53515577, +0.430958986), (+1.17242169, +0.408739328), (+1.56498945, +0.925855100), (+1.61202347, +0.691056907), (+1.42595732, +0.782053828), (+1.59482682, +0.792135596), (+1.77879596, +0.512541771), (+1.50887477, +0.577588439), (+1.60343897, +0.988416433), (+1.18402827, +0.382843137), (+1.10620046, +0.800055027), (+1.26737690, +0.585496008), (+1.46787822, +0.501343787), (+1.68477201, +0.274804890), (+1.32004058, +0.999499261), (+1.63934493, +0.137591332), (+1.93228412, +0.785169244), (+1.50438833, +0.385290921), (+1.72426677, +0.150980070), (+1.95007873, +0.426890880), (+1.44123888, +0.967406392), (+1.52670050, +0.999591768), (+1.92924881, +0.464908987), (+1.66190171, +0.203791216), (+1.84291470, +0.168471947), (+1.39693034, +0.816338360), (+1.84116673, +0.442752950E-1), (+1.42865992, +0.229278907), (+1.70166790, +0.148473354E-1), (+1.03814340, +0.315181494), (+1.05549431, +0.164465755), (+1.37814224, +0.288693815), (+1.56994724, +0.899729967), (+1.23159552, +0.842171788), (+1.21974957, +0.673607171), (+1.20658815, +0.624697208), (+1.82479978, +0.675698876)

11reltol = sqrt(epsilon(1._TKG))

12reltol

13+0.345266977E-3

14isClose(data, adat, reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, adat, reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+72

21data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

22data

23(+1.4102904366286522, +0.95284055143539892), (+1.1696856805177662, +0.66341357382418309), (+1.0191574552706715, +0.78581541984773029), (+1.6950958189661867, +0.10134304083758194), (+1.7499754562543886, +0.15716743359421970E-1), (+1.7726428170637343, +0.11327934998639488E-3), (+1.0693731876863941, +0.78498748783553340), (+1.5006426088573726, +0.47788563165630937), (+1.6075506978743852, +0.32548501709715660), (+1.0294367516333589, +0.51423955116503617), (+1.3267033962345489, +0.62532851166532655), (+1.8860646636008727, +0.21436785497219391E-1), (+1.0242864127785059, +0.87218303006232512), (+1.9102628133227524, +0.11514702067381011), (+1.6520911129393840, +0.35588077648150840), (+1.6643812596176504, +0.61592904258775449), (+1.2400703505093154, +0.97521872080975158), (+1.3365473680294175, +0.71797244107112446), (+1.7800489544918441, +0.16884381828062944), (+1.0970452203999668, +0.68537469754949865), (+1.4722645080244432, +0.12537842940779154), (+1.7651781996782803, +0.39375926049675103E-2), (+1.0064412654948502, +0.80143975202344209), (+1.2533437359060013, +0.74805059410256181), (+1.4941023171970353, +0.95457546800560955E-1), (+1.9752709520808880, +0.67431816982426340), (+1.3300168440182691, +0.89713557821070167), (+1.5032827801036568, +0.57306051505576239), (+1.4722764355050051, +0.67262483928132355), (+1.4045185810210858, +0.67793620993743942), (+1.5821981549532733, +0.54277300720230037), (+1.7689640636233539, +0.32769037680120550), (+1.4987329381138439, +0.80192647383729332), (+1.7205408283120236, +0.39483260254796382), (+1.6746777756928193, +0.85178808586521693), (+1.6802037332249073, +0.79408731149418266E-1), (+1.5323266015013515, +0.96813122248578298), (+1.0342999058517535, +0.48925432656104750), (+1.6773939570652630, +0.11440186058092394), (+1.7719746775378242, +0.21058067735328678), (+1.1902059809471854, +0.47933585893153818), (+1.0780186146713393, +0.57888038579479884), (+1.1454653484417523, +0.33779521891282682), (+1.5361805807372981, +0.37234684971497889), (+1.4579231647160644, +0.83003370662912968E-2), (+1.7144298541209690, +0.54024577729558021), (+1.8851933689720726, +0.52497974785256440), (+1.9541460081173643, +0.50509361618495396E-1), (+1.8579126684701968, +0.50836221649314772), (+1.8996876188513585, +0.98731289653321708), (+1.7519891038571420, +0.28352340517899466), (+1.7078484616886858, +0.24962393402195204), (+1.4842460154537971, +0.73406089883020897), (+1.6543261742830278, +0.26936075065767262), (+1.3670191112016352, +0.79505332423167929E-1), (+1.8160203564801534, +0.23737494026676420), (+1.8035263291875789, +0.72737440623594929), (+1.6531520840503839, +0.90838523427431039), (+1.1269881325099711, +0.47709899791737187), (+1.2129354172811566, +0.36545165756187326), (+1.6388062961191598, +0.49832237835537230), (+1.4915725382227512, +0.16475662261851909), (+1.9448271431170943, +0.92729663989500832), (+1.9671174760100480, +0.39688287390774046), (+1.8524598615107299, +0.17079755939165697), (+1.2933645022438076, +0.90106280974973685), (+1.5977743222542977, +0.92148107686702496), (+1.4283833413288778, +0.92134399012463009), (+1.3470675797031189, +0.37446750700652143), (+1.6268807626978572, +0.97172399697478007), (+1.4208127733978388, +0.11038878850595046), (+1.1235742583649682, +0.28716840249261344)

24

25adat = getFFTR(getFFTF(data)) / size(data)

26adat

27(+1.4102904366286522, +0.95284055143539903), (+1.1696856805177664, +0.66341357382418287), (+1.0191574552706713, +0.78581541984772996), (+1.6950958189661867, +0.10134304083758192), (+1.7499754562543883, +0.15716743359422008E-1), (+1.7726428170637343, +0.11327934998645656E-3), (+1.0693731876863941, +0.78498748783553340), (+1.5006426088573726, +0.47788563165630926), (+1.6075506978743848, +0.32548501709715655), (+1.0294367516333591, +0.51423955116503617), (+1.3267033962345485, +0.62532851166532655), (+1.8860646636008722, +0.21436785497219432E-1), (+1.0242864127785061, +0.87218303006232512), (+1.9102628133227526, +0.11514702067381011), (+1.6520911129393836, +0.35588077648150840), (+1.6643812596176506, +0.61592904258775460), (+1.2400703505093151, +0.97521872080975180), (+1.3365473680294173, +0.71797244107112457), (+1.7800489544918439, +0.16884381828062958), (+1.0970452203999665, +0.68537469754949865), (+1.4722645080244428, +0.12537842940779154), (+1.7651781996782803, +0.39375926049675970E-2), (+1.0064412654948502, +0.80143975202344186), (+1.2533437359060011, +0.74805059410256181), (+1.4941023171970356, +0.95457546800561011E-1), (+1.9752709520808882, +0.67431816982426340), (+1.3300168440182689, +0.89713557821070156), (+1.5032827801036570, +0.57306051505576250), (+1.4722764355050049, +0.67262483928132355), (+1.4045185810210861, +0.67793620993743942), (+1.5821981549532733, +0.54277300720230048), (+1.7689640636233535, +0.32769037680120544), (+1.4987329381138434, +0.80192647383729332), (+1.7205408283120236, +0.39483260254796404), (+1.6746777756928186, +0.85178808586521715), (+1.6802037332249067, +0.79408731149418210E-1), (+1.5323266015013512, +0.96813122248578287), (+1.0342999058517535, +0.48925432656104739), (+1.6773939570652627, +0.11440186058092389), (+1.7719746775378244, +0.21058067735328689), (+1.1902059809471852, +0.47933585893153818), (+1.0780186146713393, +0.57888038579479884), (+1.1454653484417525, +0.33779521891282666), (+1.5361805807372981, +0.37234684971497883), (+1.4579231647160638, +0.83003370662912222E-2), (+1.7144298541209690, +0.54024577729558021), (+1.8851933689720726, +0.52497974785256440), (+1.9541460081173636, +0.50509361618495549E-1), (+1.8579126684701965, +0.50836221649314794), (+1.8996876188513587, +0.98731289653321719), (+1.7519891038571416, +0.28352340517899460), (+1.7078484616886858, +0.24962393402195204), (+1.4842460154537966, +0.73406089883020897), (+1.6543261742830275, +0.26936075065767262), (+1.3670191112016354, +0.79505332423167971E-1), (+1.8160203564801531, +0.23737494026676437), (+1.8035263291875785, +0.72737440623594918), (+1.6531520840503837, +0.90838523427431050), (+1.1269881325099713, +0.47709899791737187), (+1.2129354172811564, +0.36545165756187331), (+1.6388062961191598, +0.49832237835537224), (+1.4915725382227518, +0.16475662261851895), (+1.9448271431170940, +0.92729663989500821), (+1.9671174760100480, +0.39688287390774052), (+1.8524598615107297, +0.17079755939165706), (+1.2933645022438081, +0.90106280974973707), (+1.5977743222542977, +0.92148107686702474), (+1.4283833413288776, +0.92134399012463009), (+1.3470675797031184, +0.37446750700652148), (+1.6268807626978572, +0.97172399697478029), (+1.4208127733978388, +0.11038878850595059), (+1.1235742583649677, +0.28716840249261344)

28reltol = sqrt(epsilon(1._TKG))

29reltol

30+0.14901161193847656E-7

31isClose(data, adat, reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, adat, reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+73

38data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

39data

40(+1.01166379878975613304349902663318110, +0.375448348570446385179669130015774094), (+1.46268052217274090371246940065932480, +0.882937556440435217019649967900667105), (+1.32824698191257503378067428960178028, +0.961482222378330145180357866195806093), (+1.30520025455687886997765079024387120, +0.104311987192482218896108445208851550), (+1.61664657171610666004149891701198096, +0.516670779043636068716057231595327897), (+1.27792888794185991396361275521788759, +0.288980909280290155102373899003270215), (+1.62391645152374681540827351202859953, +0.110840700828607854821606832109377698), (+1.10979365850462071718038328231340518, +0.464329184731001852736849760413914975), (+1.69257972006765764158423512850883522, +0.619960691419439846119854863234480345), (+1.83572141638899272227072464377154561, +0.672885743585831626156024121573250469), (+1.07950627684706915839519837006803818, +0.644407467804076428758889058638537908), (+1.31691900301194400139825225118422211, +0.545032029171919548629463582861356642E-1), (+1.58282354315561696410953203982022821, +0.246474370156350943526124440833919873), (+1.20954865823757687836859343098190972, +0.224046628873811549234053347142045925), (+1.23013092328782256852631459710852714, +0.254259127754621465475727928453186569), (+1.60766822987372452085917841917612230, +0.968690266688225172882512680833891475E-1), (+1.60801707171102543979216016621948704, +0.820792976591261411243590739991061288), (+1.65396851495453470219317751160577852, +0.399295815532165779455877633953399780), (+1.66456070822550275513917856412127272, +0.129287484377623236094805010774840855), (+1.34262178824313095366324725057660514, +0.733656518806066089826003321360502867), (+1.28763787991538719101716942405791770, +0.883167804512824102579078579213931994E-1), (+1.63517627011926172572844854406145181, +0.349335817583617327948216812210813705), (+1.62742182968262821180938447434131563, +0.618105860348516516906225950478267604), (+1.68677413993884185793738382643149097, +0.440766032775849112387716783589757541), (+1.72481775736463623665668864526515403, +0.961935202283263953654650808220769230), (+1.22220222779005342003562726186583049, +0.855616772750615117687659643530130528E-1), (+1.13748334849771577064290523591885076, +0.528933901437922154842643554215635329), (+1.08989477110607207412791852015183705, +0.851703103727692458264500276847142338), (+1.23618916666483761726499841098033406, +0.936330262487984791743766298450905347), (+1.02027495165442916001335373463035287, +0.333514453432326686192390838500120634), (+1.33000609329181025222996885799852050, +0.698337820847301025138315816656390885), (+1.44256491481402639808828954839236079, +0.540601765030107029171461424491702443), (+1.42682185462842974395427975415551150, +0.259999988373108411495631981981237110), (+1.55026872847448422746571656085328563, +0.447941668481482442180734842543975040), (+1.51567774809465012707464453467934480, +0.556753042001921223182510711544403967E-1), (+1.15281720108050698358187208506392031, +0.711376503266183297204981120843971215), (+1.90885206568113382080249359744296928, +0.902516146421065564618212803393905075), (+1.51980056269819680113219267704183140, +0.787569294722848463197916705919735354E-1), (+1.80753419197900163376478563521779100, +0.876653009925187799020451582014707516), (+1.84654346508799302961575336127705510, +0.939316460724937831485127082626561424), (+1.27803123000702386258822713104242376, +0.274808149550130579979076586779934594), (+1.18993663492986803682202079909696941, +0.327066644267082005302469969650226151), (+1.31561607356513465329675714639258811, +0.515480863795623278160321400826038570E-1), (+1.51732007733704922209267846004394050, +0.728356959544295392388596748187869380), (+1.56777146052801831777212641646303094, +0.770889186373031509765765642814032179), (+1.91226040062782617217179768169935246, +0.532409654917788818382494418530926514), (+1.01123548403286749328225373791198190, +0.309470532068826725007027410517177265), (+1.32563379268191838785953787445936126, +0.302408147028726935810208573047568358), (+1.93224397287025735538000210642282852, +0.631535973983290575917625987309821293), (+1.58058343660941375380600260242465269, +0.554296128176052608082098962793637260), (+1.26483297409475945330890990942256258, +0.828928396467756337455224997803041413), (+1.10200878517792888911895753375939880, +0.398965462909793299040514063845788780E-1), (+1.95737948840045370028936338485778632, +0.547614150515474454018111604105697294), (+1.36780468191226813795179485630467635, +0.608637217877164798184765121269675612), (+1.80904865369139098136607915505145528, +0.118906475258115827690252389914973537), (+1.02032616970773069991577278631588067, +0.137654783352222661722118072038859338), (+1.99052507580332978371631972261234027, +0.258883780971506403652739368072220377), (+1.48773210593174920243383901235407313, +0.645072904395440038631418904508074544), (+1.66866466830703574979633914636339595, +0.474901756249267996318185405162225262), (+1.12047977502675425512797122614232281, +0.665442730735921596430132893511795353), (+1.44969417886927031619532418849209481, +0.479403036987099269243428606978163680), (+1.71704176859179523466932283718741526, +0.908372853488310717662860951931626626), (+1.23200699298586913589910555302344938, +0.962617019391251497046633023869587247), (+1.33427007964964098780591282427116479, +0.444971454930090583834205572383153260E-1), (+1.40358930302887011059246953410997775, +0.606619570323071388341406710184847031), (+1.91462429896020056367201968412084321, +0.512722165543035921154482923230036539), (+1.51731690521453374358065760631643187, +0.840029223962060845308394671569974912), (+1.76060927488295591027344510671880838, +0.482559880174137618500380666284171768), (+1.67579823651131627559496762675874640, +0.651591140376924693497805023534419242), (+1.28743913291956660347994827853513136, +0.127496061877367295098521690451287184), (+1.45116262590440866113821039699397229, +0.206777449554610913226828556356920318), (+1.32294124348057742131717056127432794, +0.597754277365914968320600385386072267), (+1.44500247721648106670308067077543604, +0.923561864474191656233742216614911192)

41

42adat = getFFTR(getFFTF(data)) / size(data)

43adat

44(+1.01166379878975613304349902663317340, +0.375448348570446385179669130015771398), (+1.46268052217274090371246940065932577, +0.882937556440435217019649967900667105), (+1.32824698191257503378067428960178066, +0.961482222378330145180357866195806478), (+1.30520025455687886997765079024387197, +0.104311987192482218896108445208851695), (+1.61664657171610666004149891701198154, +0.516670779043636068716057231595327801), (+1.27792888794185991396361275521788797, +0.288980909280290155102373899003270167), (+1.62391645152374681540827351202860011, +0.110840700828607854821606832109378144), (+1.10979365850462071718038328231340576, +0.464329184731001852736849760413915023), (+1.69257972006765764158423512850883599, +0.619960691419439846119854863234480345), (+1.83572141638899272227072464377154600, +0.672885743585831626156024121573250180), (+1.07950627684706915839519837006803856, +0.644407467804076428758889058638538101), (+1.31691900301194400139825225118422191, +0.545032029171919548629463582861356281E-1), (+1.58282354315561696410953203982022841, +0.246474370156350943526124440833919897), (+1.20954865823757687836859343098190972, +0.224046628873811549234053347142046069), (+1.23013092328782256852631459710852752, +0.254259127754621465475727928453186136), (+1.60766822987372452085917841917612230, +0.968690266688225172882512680833890994E-1), (+1.60801707171102543979216016621948685, +0.820792976591261411243590739991061576), (+1.65396851495453470219317751160577852, +0.399295815532165779455877633953399828), (+1.66456070822550275513917856412127368, +0.129287484377623236094805010774840976), (+1.34262178824313095366324725057660591, +0.733656518806066089826003321360502771), (+1.28763787991538719101716942405791770, +0.883167804512824102579078579213930429E-1), (+1.63517627011926172572844854406145297, +0.349335817583617327948216812210813561), (+1.62742182968262821180938447434131679, +0.618105860348516516906225950478267796), (+1.68677413993884185793738382643149097, +0.440766032775849112387716783589757541), (+1.72481775736463623665668864526515480, +0.961935202283263953654650808220769326), (+1.22220222779005342003562726186583106, +0.855616772750615117687659643530130889E-1), (+1.13748334849771577064290523591885114, +0.528933901437922154842643554215635618), (+1.08989477110607207412791852015183666, +0.851703103727692458264500276847142531), (+1.23618916666483761726499841098033444, +0.936330262487984791743766298450905829), (+1.02027495165442916001335373463035287, +0.333514453432326686192390838500120682), (+1.33000609329181025222996885799852127, +0.698337820847301025138315816656390885), (+1.44256491481402639808828954839236137, +0.540601765030107029171461424491702828), (+1.42682185462842974395427975415551169, +0.259999988373108411495631981981237014), (+1.55026872847448422746571656085328563, +0.447941668481482442180734842543974992), (+1.51567774809465012707464453467934441, +0.556753042001921223182510711544406375E-1), (+1.15281720108050698358187208506392031, +0.711376503266183297204981120843971311), (+1.90885206568113382080249359744296851, +0.902516146421065564618212803393904882), (+1.51980056269819680113219267704183063, +0.787569294722848463197916705919731382E-1), (+1.80753419197900163376478563521779119, +0.876653009925187799020451582014707612), (+1.84654346508799302961575336127705472, +0.939316460724937831485127082626561232), (+1.27803123000702386258822713104242376, +0.274808149550130579979076586779934546), (+1.18993663492986803682202079909696960, +0.327066644267082005302469969650226007), (+1.31561607356513465329675714639258888, +0.515480863795623278160321400826039713E-1), (+1.51732007733704922209267846004394127, +0.728356959544295392388596748187869187), (+1.56777146052801831777212641646303075, +0.770889186373031509765765642814032564), (+1.91226040062782617217179768169935246, +0.532409654917788818382494418530926803), (+1.01123548403286749328225373791198151, +0.309470532068826725007027410517177409), (+1.32563379268191838785953787445936145, +0.302408147028726935810208573047568647), (+1.93224397287025735538000210642282929, +0.631535973983290575917625987309821196), (+1.58058343660941375380600260242465308, +0.554296128176052608082098962793637260), (+1.26483297409475945330890990942256278, +0.828928396467756337455224997803041509), (+1.10200878517792888911895753375939976, +0.398965462909793299040514063845790285E-1), (+1.95737948840045370028936338485778748, +0.547614150515474454018111604105697391), (+1.36780468191226813795179485630467635, +0.608637217877164798184765121269675419), (+1.80904865369139098136607915505145625, +0.118906475258115827690252389914973681), (+1.02032616970773069991577278631588105, +0.137654783352222661722118072038859386), (+1.99052507580332978371631972261234007, +0.258883780971506403652739368072220666), (+1.48773210593174920243383901235407294, +0.645072904395440038631418904508074640), (+1.66866466830703574979633914636339595, +0.474901756249267996318185405162225118), (+1.12047977502675425512797122614232339, +0.665442730735921596430132893511795353), (+1.44969417886927031619532418849209500, +0.479403036987099269243428606978163776), (+1.71704176859179523466932283718741526, +0.908372853488310717662860951931626722), (+1.23200699298586913589910555302344918, +0.962617019391251497046633023869587247), (+1.33427007964964098780591282427116498, +0.444971454930090583834205572383155427E-1), (+1.40358930302887011059246953410997794, +0.606619570323071388341406710184846935), (+1.91462429896020056367201968412084378, +0.512722165543035921154482923230036442), (+1.51731690521453374358065760631643284, +0.840029223962060845308394671569975297), (+1.76060927488295591027344510671880857, +0.482559880174137618500380666284172249), (+1.67579823651131627559496762675874697, +0.651591140376924693497805023534419146), (+1.28743913291956660347994827853513232, +0.127496061877367295098521690451287063), (+1.45116262590440866113821039699397287, +0.206777449554610913226828556356920631), (+1.32294124348057742131717056127432833, +0.597754277365914968320600385386072555), (+1.44500247721648106670308067077543700, +0.923561864474191656233742216614911480)

45reltol = sqrt(epsilon(1._TKG))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, adat, reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, adat, reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+82

55data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

56data

57+1.86321259, +1.15817666, +1.92555869, +1.00200129, +1.55059552, +1.43150604, +1.37131786, +1.45487499, +1.84691334, +1.00765836, +1.42405581, +1.39109731, +1.04707491, +1.30797887, +1.64327502, +1.32482171, +1.79821646, +1.07285535, +1.01757002, +1.36514306, +1.52039027, +1.66797709, +1.37520170, +1.12192106, +1.08986378, +1.72206163, +1.66064143, +1.96982181, +1.54550862, +1.69002891, +1.91208601, +1.78330994, +1.86620784, +1.22001362, +1.25038695, +1.64968395, +1.76812863, +1.29913938, +1.23657513, +1.80242038, +1.36953545, +1.93289638, +1.74014056, +1.83142114, +1.72535634, +1.59136558, +1.10146356, +1.64828765, +1.25151932, +1.58535719, +1.47601008, +1.21056485, +1.98414671, +1.95520282, +1.71292198, +1.30001020, +1.58264613, +1.43914437, +1.77502441, +1.22593880, +1.28220749, +1.41413748, +1.96660542, +1.67568696, +1.97968268, +1.86943126, +1.68616414, +1.29441202, +1.49696159, +1.53416252, +1.22466016, +1.46979046, +1.48269391, +1.72627604, +1.24316859, +1.52036762, +1.03836060, +1.31579471, +1.71728373, +1.91972244, +1.74963188, +1.36343098

58

59adat = getFFTR(getFFTF(data)) / size(data)

60adat

61+1.86321294, +1.15817666, +1.92555797, +1.00200093, +1.55059552, +1.43150568, +1.37131751, +1.45487463, +1.84691286, +1.00765872, +1.42405498, +1.39109719, +1.04707575, +1.30797911, +1.64327431, +1.32482171, +1.79821610, +1.07285571, +1.01756990, +1.36514306, +1.52039063, +1.66797698, +1.37520158, +1.12192166, +1.08986521, +1.72206211, +1.66064131, +1.96982205, +1.54550922, +1.69002926, +1.91208446, +1.78330958, +1.86620772, +1.22001445, +1.25038660, +1.64968216, +1.76812887, +1.29914093, +1.23657310, +1.80241728, +1.36954081, +1.93290174, +1.74014544, +1.83142626, +1.72535264, +1.59136331, +1.10146523, +1.64828861, +1.25151813, +1.58535564, +1.47601128, +1.21056533, +1.98414505, +1.95520210, +1.71292281, +1.30001068, +1.58264589, +1.43914521, +1.77502501, +1.22593999, +1.28220761, +1.41413772, +1.96660554, +1.67568707, +1.97968149, +1.86943054, +1.68616450, +1.29441237, +1.49696112, +1.53416228, +1.22466087, +1.46979094, +1.48269296, +1.72627556, +1.24316883, +1.52036762, +1.03836036, +1.31579483, +1.71728373, +1.91972220, +1.74963117, +1.36343062

62reltol = sqrt(epsilon(1._TKG))

63reltol

64+0.345266977E-3

65isClose(data, adat, reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, adat, reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+20

72data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

73data

74+1.1572008274651315, +1.6858743406727554, +1.2931730527535086, +1.5382855791137766, +1.3828798054666513, +1.5630993065984606, +1.4489171443438245, +1.1797377530267257, +1.7130394970413718, +1.9402538406571654, +1.1588039492428579, +1.3721872488097560, +1.4998049732090086, +1.3225063323313124, +1.1573712481890963, +1.8545263855564511, +1.8825913386213453, +1.3806423632589861, +1.6345067146582384, +1.3681911225087353

75

76adat = getFFTR(getFFTF(data)) / size(data)

77adat

78+1.1572008274651320, +1.6858743406727559, +1.2931730527535092, +1.5382855791137771, +1.3828798054666511, +1.5630993065984606, +1.4489171443438247, +1.1797377530267255, +1.7130394970413718, +1.9402538406571654, +1.1588039492428579, +1.3721872488097557, +1.4998049732090089, +1.3225063323313127, +1.1573712481890963, +1.8545263855564511, +1.8825913386213451, +1.3806423632589864, +1.6345067146582388, +1.3681911225087351

79reltol = sqrt(epsilon(1._TKG))

80reltol

81+0.14901161193847656E-7

82isClose(data, adat, reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, adat, reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+79

89data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

90data

91+1.08357492549454685837098841270193997, +1.77340145012427586938208780297208975, +1.84830148288299871318470656056851057, +1.69291710281794000954911410671715044, +1.77987011544527894969932581889942940, +1.48581739362727079284357423243987106, +1.35692648687834095412626760365315246, +1.09450682865217141956503435130521159, +1.76304054943471312498874518434534688, +1.39484910845502745619660105579024606, +1.61988917075276411335064363488135860, +1.97484021064535605985430527139237873, +1.08402812268366919397599733774293382, +1.38603108438118479381778739871294355, +1.86058649944420717766164518920255958, +1.80439834336189960232496622440925794, +1.69281177912480556121483549757179801, +1.02333337224510276488391489776233072, +1.85366050383596279494819805920554281, +1.80213781585394627787095267597609182, +1.83346613134791721183387571244484771, +1.93692291221538994642849691285889519, +1.31945604217512855820546843611766804, +1.09574740225469158706673161680150812, +1.21788718955978034176429751778393190, +1.59770968633365104517147202661044171, +1.68397369893569395242747029077602067, +1.37911446544846298920609079404146779, +1.11649806124507935985538941847178976, +1.84372582576297893063284956205646205, +1.06907782419405868012735380110300145, +1.38732187717820232982648011421542007, +1.09866554962337870434338950165135263, +1.67069306015468940630156231469525108, +1.44496767174467495381528651597640434, +1.55240246883639766434887609144681496, +1.33499086072031536029025977776510852, +1.64999070698191661574209545398330976, +1.94778188062712614464671106725042665, +1.36445838658762852399486731303097163, +1.64543386448232677703783810608492696, +1.05282270752036596376042640266632195, +1.18064596420356017852998960925634880, +1.45254740932247036776912559882099332, +1.44581023367524224238054132110713358, +1.45570393392772911296012010539612707, +1.72897658180539708386593390608347269, +1.82611260988532910881839029438581594, +1.90909596730838500517157236751816523, +1.09883583397082624189851804633108868, +1.12462224847402460089817741704360894, +1.14712012319526716717381137425842255, +1.00268092039625088594473346493956592, +1.86868029481122137383905728581733837, +1.15322350600921005092601189907960393, +1.59439022522600180630056700129364045, +1.16633498175764752802888949628928263, +1.09000458006262618811012634681479991, +1.25003223329906191051547101353502820, +1.20471342689012565982496833552503541, +1.40215106866636808809055991339096655, +1.64586812566626985106003484455837414, +1.09791910040055302186868582285162233, +1.03986640154807109557554604836598026, +1.64686617346943540334772294092643378, +1.25557934230344675575028665715718462, +1.42348734150869956698252028094159158, +1.44028086140347378075926993402153759, +1.71977798816727784957889540034033585, +1.29378634081316905903881113984890469, +1.45429797417298485249620431753913804, +1.33667949503897372149849843216336927, +1.75347774163567440798525205196046328, +1.29644044767329947950821573484566915, +1.72343996331520255248584499177423614, +1.11547255209504689220394744653221837, +1.95815962683231442706833238674432451, +1.77140140903491003051258930304036454, +1.17989788286122931586921483372003113

92

93adat = getFFTR(getFFTF(data)) / size(data)

94adat

95+1.08357492549454685837098841270194228, +1.77340145012427586938208780297209109, +1.84830148288299871318470656056851192, +1.69291710281794000954911410671715198, +1.77987011544527894969932581889942921, +1.48581739362727079284357423243987299, +1.35692648687834095412626760365315265, +1.09450682865217141956503435130521853, +1.76304054943471312498874518434534225, +1.39484910845502745619660105579024972, +1.61988917075276411335064363488135995, +1.97484021064535605985430527139237006, +1.08402812268366919397599733774294325, +1.38603108438118479381778739871294836, +1.86058649944420717766164518920255419, +1.80439834336189960232496622440925621, +1.69281177912480556121483549757179281, +1.02333337224510276488391489776234921, +1.85366050383596279494819805920553299, +1.80213781585394627787095267597608971, +1.83346613134791721183387571244484366, +1.93692291221538994642849691285888364, +1.31945604217512855820546843611767402, +1.09574740225469158706673161680151698, +1.21788718955978034176429751778393806, +1.59770968633365104517147202661043651, +1.68397369893569395242747029077601316, +1.37911446544846298920609079404146798, +1.11649806124507935985538941847180613, +1.84372582576297893063284956205643778, +1.06907782419405868012735380110302071, +1.38732187717820232982648011421541391, +1.09866554962337870434338950165136900, +1.67069306015468940630156231469523683, +1.44496767174467495381528651597640511, +1.55240246883639766434887609144680745, +1.33499086072031536029025977776511526, +1.64999070698191661574209545398330571, +1.94778188062712614464671106725040296, +1.36445838658762852399486731303098954, +1.64543386448232677703783810608491386, +1.05282270752036596376042640266633909, +1.18064596420356017852998960925635477, +1.45254740932247036776912559882098658, +1.44581023367524224238054132110713204, +1.45570393392772911296012010539612823, +1.72897658180539708386593390608346614, +1.82611260988532910881839029438580882, +1.90909596730838500517157236751814635, +1.09883583397082624189851804633110332, +1.12462224847402460089817741704361414, +1.14712012319526716717381137425842466, +1.00268092039625088594473346493958171, +1.86868029481122137383905728581731449, +1.15322350600921005092601189907961934, +1.59439022522600180630056700129362793, +1.16633498175764752802888949628928764, +1.09000458006262618811012634681480396, +1.25003223329906191051547101353502723, +1.20471342689012565982496833552503791, +1.40215106866636808809055991339096617, +1.64586812566626985106003484455836470, +1.09791910040055302186868582285162907, +1.03986640154807109557554604836598796, +1.64686617346943540334772294092642435, +1.25557934230344675575028665715718924, +1.42348734150869956698252028094159177, +1.44028086140347378075926993402153952, +1.71977798816727784957889540034033181, +1.29378634081316905903881113984890970, +1.45429797417298485249620431753913727, +1.33667949503897372149849843216337216, +1.75347774163567440798525205196046020, +1.29644044767329947950821573484567377, +1.72343996331520255248584499177423421, +1.11547255209504689220394744653222376, +1.95815962683231442706833238674432316, +1.77140140903491003051258930304036589, +1.17989788286122931586921483372003306

96reltol = sqrt(epsilon(1._TKG))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, adat, reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, adat, reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+75

106data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

107data

108(+1.64316607, +0.538386464), (+1.67978168, +0.668041825), (+1.52408957, +0.816679478), (+1.46817374, +0.358178735), (+1.02314377, +0.828818262), (+1.60575998, +0.121988177), (+1.29649854, +0.348889709), (+1.50394201, +0.189079821), (+1.03180671, +0.125023842), (+1.60115600, +0.925370574), (+1.90753794, +0.540531695), (+1.15660787, +0.566443563), (+1.81601644, +0.270528436), (+1.72856164, +0.845070541), (+1.56085145, +0.791744173), (+1.81884682, +0.651183665), (+1.63918543, +0.215551496), (+1.97628105, +0.827456236), (+1.08431053, +0.239370465E-1), (+1.09297347, +0.382888138), (+1.66793644, +0.399884939), (+1.97093105, +0.116075456), (+1.97733450, +0.643505156), (+1.53030419, +0.809161603), (+1.58365929, +0.188488543), (+1.22336459, +0.760752201), (+1.84696054, +0.178471684), (+1.86353159, +0.715820372), (+1.72342658, +0.196548402), (+1.32456160, +0.683808208), (+1.06868100, +0.182313263), (+1.00809646, +0.287978590), (+1.57209301, +0.425250053), (+1.66381538, +0.355942667), (+1.49814010, +0.463459015), (+1.33786845, +0.354465365), (+1.09418797, +0.696612239), (+1.15977108, +0.327597499), (+1.35697436, +0.111560225E-1), (+1.04462242, +0.692109644), (+1.09231532, +0.756366968), (+1.92571497, +0.763425231), (+1.27759361, +0.859137297), (+1.39007545, +0.729673803), (+1.48080039, +0.197346807E-1), (+1.86601543, +0.236360252), (+1.31451178, +0.929642320E-1), (+1.39254308, +0.696119785), (+1.38475752, +0.505411029E-1), (+1.05203056, +0.853584170), (+1.60020411, +0.323768258E-1), (+1.29858375, +0.774504781), (+1.93106878, +0.102080226), (+1.20302546, +0.603254437), (+1.61222386, +0.394400537), (+1.03724670, +0.177201927), (+1.61258268, +0.651113451), (+1.09318101, +0.655171633), (+1.04221582, +0.447958112), (+1.81952953, +0.151124358), (+1.90736365, +0.581203520), (+1.77153158, +0.981588840), (+1.82871318, +0.520531774), (+1.44988310, +0.700605989), (+1.27613521, +0.728921890E-1), (+1.60944879, +0.316374660), (+1.33055103, +0.527516842), (+1.19204807, +0.667843878), (+1.94165611, +0.910869300), (+1.14657569, +0.922776163), (+1.91202652, +0.646254599), (+1.51172876, +0.366974175), (+1.46400523, +0.711630404), (+1.14939916, +0.114386082), (+1.28830409, +0.282115579)

109

110adat = getFFTR(getFFTF(data)) / size(data)

111adat

112(+1.64316559, +0.538386285), (+1.67978144, +0.668041766), (+1.52408957, +0.816679537), (+1.46817350, +0.358178824), (+1.02314353, +0.828818142), (+1.60575974, +0.121988043), (+1.29649866, +0.348889709), (+1.50394201, +0.189079896), (+1.03180659, +0.125023901), (+1.60115588, +0.925370693), (+1.90753758, +0.540531695), (+1.15660787, +0.566443563), (+1.81601644, +0.270528436), (+1.72856176, +0.845070601), (+1.56085145, +0.791744173), (+1.81884658, +0.651183546), (+1.63918531, +0.215551525), (+1.97628117, +0.827456295), (+1.08431065, +0.239371751E-1), (+1.09297359, +0.382888138), (+1.66793609, +0.399884850), (+1.97093117, +0.116075441), (+1.97733462, +0.643505216), (+1.53030396, +0.809161842), (+1.58365941, +0.188488662), (+1.22336400, +0.760752082), (+1.84696043, +0.178471655), (+1.86353147, +0.715820432), (+1.72342634, +0.196548283), (+1.32456160, +0.683808148), (+1.06868076, +0.182313129), (+1.00809658, +0.287978619), (+1.57209325, +0.425249994), (+1.66381562, +0.355942816), (+1.49814022, +0.463459074), (+1.33786821, +0.354465216), (+1.09418809, +0.696612358), (+1.15977097, +0.327597439), (+1.35697448, +0.111561073E-1), (+1.04462230, +0.692109585), (+1.09231508, +0.756366968), (+1.92571509, +0.763425231), (+1.27759373, +0.859137475), (+1.39007556, +0.729673803), (+1.48080051, +0.197346043E-1), (+1.86601520, +0.236360118), (+1.31451178, +0.929641873E-1), (+1.39254308, +0.696119726), (+1.38475764, +0.505411029E-1), (+1.05203032, +0.853584170), (+1.60020387, +0.323766693E-1), (+1.29858363, +0.774504781), (+1.93106854, +0.102080293), (+1.20302534, +0.603254378), (+1.61222363, +0.394400537), (+1.03724635, +0.177201867), (+1.61258280, +0.651113510), (+1.09318113, +0.655171812), (+1.04221570, +0.447958022), (+1.81952965, +0.151124418), (+1.90736353, +0.581203341), (+1.77153158, +0.981588840), (+1.82871318, +0.520531774), (+1.44988346, +0.700605989), (+1.27613521, +0.728922933E-1), (+1.60944855, +0.316374600), (+1.33055115, +0.527516842), (+1.19204819, +0.667843878), (+1.94165611, +0.910869539), (+1.14657569, +0.922775984), (+1.91202617, +0.646254480), (+1.51172876, +0.366974205), (+1.46400523, +0.711630464), (+1.14939904, +0.114386111), (+1.28830421, +0.282115519)

113reltol = sqrt(epsilon(1._TKG))

114reltol

115+0.345266977E-3

116isClose(data, adat, reltol = reltol)

117T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

118call setAsserted(all(isClose(data, adat, reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+80

123data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

124data

125(+1.9838995596547688, +0.84074915617373069), (+1.8011736637306415, +0.75032726358856061), (+1.7981631205189323, +0.18681246480835023E-2), (+1.4002740759492269, +0.78370416824297762), (+1.8046045759319780, +0.16772496378648083E-1), (+1.8916792076994202, +0.29117844194206621), (+1.5684967087377584, +0.37449474689064433), (+1.5520928859669967, +0.69566744499669930), (+1.1913614463488782, +0.58615984205137117), (+1.8511742151718460, +0.27902277501946804), (+1.6805792147691252, +0.66865613650612299), (+1.0848807899662483, +0.42853720036076492), (+1.2067059807663889, +0.13600953170001606), (+1.5614072308015308, +0.31378864550709706E-1), (+1.1742915577525705, +0.57301211170286892), (+1.7622388479734266, +0.13742276372795126E-1), (+1.1476137589144777, +0.73232827283260393), (+1.9829474197342956, +0.73703810183539209), (+1.8090058347876381, +0.71414424270709864), (+1.2533424924064684, +0.67659596475115280), (+1.4997481598559963, +0.22170817312280666), (+1.5768962618196227, +0.34335521305675110), (+1.0188810547833564, +0.85842936113786839), (+1.2249339022429948, +0.48436522349853250), (+1.7857207859856512, +0.80961813176465713), (+1.9301250887801549, +0.92040312863203488), (+1.0954583375129416, +0.47330593602300930), (+1.6683108829470734, +0.29301073989981652), (+1.6612246182955654, +0.10638966208845857), (+1.8090412381090590, +0.91846769232924574), (+1.7730618339026469, +0.80094258385750683E-1), (+1.7885033740859133, +0.66692743629742146), (+1.2960766592062678, +0.20692917703449210), (+1.7423369253485064, +0.65528002911943639), (+1.7208776170664866, +0.51829869522941208), (+1.9867922849018447, +0.69490019347332999), (+1.0635248816608467, +0.53933982545442127), (+1.7989480806044855, +0.80742029899392997), (+1.9175211990913397, +0.45352987639891773), (+1.3922294853595991, +0.24142465092596044), (+1.3724441757485999, +0.47371625797535966), (+1.3119444271634659, +0.24841970802472346), (+1.5636007336196913, +0.69357270662482629), (+1.3440235054073733, +0.14072231494100307E-1), (+1.6043868635998928, +0.69505863439914739), (+1.5725858817584952, +0.46737873525699802E-1), (+1.3383113432053015, +0.94292580199818177), (+1.1663754148444609, +0.49087738227228694), (+1.0254422423717311, +0.36950383194741487), (+1.3142407263856786, +0.60229998981248556), (+1.0304717971789934, +0.81157887621715963), (+1.2072435949547620, +0.74841390584030310), (+1.4984702676040598, +0.98190639255099055), (+1.4433650856444751, +0.41413548523278276E-1), (+1.4513912965962172, +0.48581112800879389), (+1.0521058097800255, +0.16408863178855204), (+1.8128966982376213, +0.39070734727887713), (+1.4637420030186843, +0.82221470630225224), (+1.1732391595521965, +0.69324375740370181), (+1.0356401897155352, +0.51775004666258895), (+1.3454417329343120, +0.86583001951672600), (+1.0130005262582613, +0.46867946826850004), (+1.8037513514135017, +0.78751974503015554), (+1.8145262930940425, +0.65786819318691914), (+1.2077606839689348, +0.97896705581785615), (+1.0758728609236150, +0.90351886814638127), (+1.7747474504745386, +0.10914647768833652), (+1.8029736509829717, +0.30966429269310924), (+1.2777210888350374, +0.54837374368695402E-1), (+1.3752222119348549, +0.51333975782390073E-1), (+1.7382917203004991, +0.23018173748650339), (+1.2400360875213505, +0.45420179138397199), (+1.9583818488012057, +0.21854505233237476), (+1.7184339076554380, +0.55169358217177311), (+1.0507763603909730, +0.13179939994565615), (+1.4991105489219188, +0.67625048001610732), (+1.0986535681764018, +0.59687827265696658), (+1.8089357581414389, +0.67206992552185518), (+1.0044635530417798, +0.58979092546293721), (+1.8723975004069162, +0.17245575810107439)

126

127adat = getFFTR(getFFTF(data)) / size(data)

128adat

129(+1.9838995596547693, +0.84074915617373081), (+1.8011736637306413, +0.75032726358856061), (+1.7981631205189319, +0.18681246480835912E-2), (+1.4002740759492265, +0.78370416824297762), (+1.8046045759319782, +0.16772496378648149E-1), (+1.8916792076994207, +0.29117844194206632), (+1.5684967087377584, +0.37449474689064444), (+1.5520928859669969, +0.69566744499669930), (+1.1913614463488778, +0.58615984205137128), (+1.8511742151718458, +0.27902277501946815), (+1.6805792147691254, +0.66865613650612321), (+1.0848807899662478, +0.42853720036076498), (+1.2067059807663887, +0.13600953170001623), (+1.5614072308015303, +0.31378864550709727E-1), (+1.1742915577525705, +0.57301211170286881), (+1.7622388479734270, +0.13742276372795103E-1), (+1.1476137589144781, +0.73232827283260393), (+1.9829474197342951, +0.73703810183539198), (+1.8090058347876377, +0.71414424270709875), (+1.2533424924064684, +0.67659596475115302), (+1.4997481598559967, +0.22170817312280691), (+1.5768962618196227, +0.34335521305675121), (+1.0188810547833562, +0.85842936113786839), (+1.2249339022429946, +0.48436522349853262), (+1.7857207859856512, +0.80961813176465713), (+1.9301250887801551, +0.92040312863203511), (+1.0954583375129414, +0.47330593602300935), (+1.6683108829470732, +0.29301073989981663), (+1.6612246182955652, +0.10638966208845861), (+1.8090412381090590, +0.91846769232924574), (+1.7730618339026478, +0.80094258385750766E-1), (+1.7885033740859133, +0.66692743629742179), (+1.2960766592062676, +0.20692917703449210), (+1.7423369253485057, +0.65528002911943661), (+1.7208776170664870, +0.51829869522941230), (+1.9867922849018449, +0.69490019347332999), (+1.0635248816608467, +0.53933982545442150), (+1.7989480806044849, +0.80742029899393020), (+1.9175211990913392, +0.45352987639891779), (+1.3922294853595993, +0.24142465092596033), (+1.3724441757486001, +0.47371625797535977), (+1.3119444271634657, +0.24841970802472374), (+1.5636007336196911, +0.69357270662482651), (+1.3440235054073726, +0.14072231494100284E-1), (+1.6043868635998930, +0.69505863439914750), (+1.5725858817584952, +0.46737873525699983E-1), (+1.3383113432053015, +0.94292580199818199), (+1.1663754148444609, +0.49087738227228706), (+1.0254422423717309, +0.36950383194741498), (+1.3142407263856783, +0.60229998981248567), (+1.0304717971789938, +0.81157887621715974), (+1.2072435949547620, +0.74841390584030321), (+1.4984702676040595, +0.98190639255099088), (+1.4433650856444744, +0.41413548523278235E-1), (+1.4513912965962172, +0.48581112800879406), (+1.0521058097800260, +0.16408863178855210), (+1.8128966982376213, +0.39070734727887702), (+1.4637420030186841, +0.82221470630225224), (+1.1732391595521960, +0.69324375740370159), (+1.0356401897155352, +0.51775004666258917), (+1.3454417329343120, +0.86583001951672622), (+1.0130005262582613, +0.46867946826850027), (+1.8037513514135015, +0.78751974503015565), (+1.8145262930940422, +0.65786819318691880), (+1.2077606839689352, +0.97896705581785626), (+1.0758728609236148, +0.90351886814638127), (+1.7747474504745380, +0.10914647768833641), (+1.8029736509829717, +0.30966429269310919), (+1.2777210888350372, +0.54837374368695443E-1), (+1.3752222119348549, +0.51333975782390164E-1), (+1.7382917203004997, +0.23018173748650345), (+1.2400360875213505, +0.45420179138397215), (+1.9583818488012052, +0.21854505233237478), (+1.7184339076554374, +0.55169358217177311), (+1.0507763603909732, +0.13179939994565629), (+1.4991105489219188, +0.67625048001610755), (+1.0986535681764018, +0.59687827265696647), (+1.8089357581414387, +0.67206992552185507), (+1.0044635530417794, +0.58979092546293721), (+1.8723975004069164, +0.17245575810107430)

130reltol = sqrt(epsilon(1._TKG))

131reltol

132+0.14901161193847656E-7

133isClose(data, adat, reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, adat, reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+74

140data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

141data

142(+1.48912045318769675155132589246311042, +0.914307180470642470374057901579121088), (+1.06780130203332572381004744614804589, +0.287195640566712012176812545271084713), (+1.95078762934547436440589617404764274, +0.353016097909431550029843777591644661), (+1.89391095336954232005780173177661763, +0.835847469201370681093420897266977751), (+1.19473482509093926218753349250064289, +0.707963309115863378785890868333808355), (+1.19995921255796866980450645612351567, +0.269385685353125133085763591663619414), (+1.47835649561370204716972628397914730, +0.710888373492738406877804566841618761), (+1.16842363745638728893249175968680315, +0.996768559415545672804870508827342333), (+1.53832350339495799859929124047515883, +0.967505217332575329093715940365578304), (+1.75643706011308950486474648193471416, +0.495096105149147844491019168633712150E-1), (+1.27642218499052027671376701457923826, +0.337099889043289042093571065706280778), (+1.87458930242951756406303931072893929, +0.450171938699994300834295678555055022), (+1.23650833534106086733962618997778627, +0.284783162243330904888146312077918951E-1), (+1.06002156190256418074375401234385349, +0.264033027667058287771230900202623719), (+1.24208135925346567268430952831281502, +0.594237234834116822525772044342632948), (+1.84629298154802038380631437110517710, +0.808950767742248492806966410808595243), (+1.28101381891181917214220416967216465, +0.671772131477051665097962783143572251E-1), (+1.51608214693430740454173463534331637, +0.328798315921688663958753149688866592E-1), (+1.50026169956443829908007063430204268, +0.750515545346938125569652110708923499), (+1.50248358930734418997845964342914688, +0.491264222015660866610450713227405937E-1), (+1.20550150856410990993938244185823592, +0.199477467182020520265323562815405385), (+1.67582629910434113851807902073754789, +0.962844817896523712045597921246430246), (+1.87340473466396799961259185424063741, +0.234945333069173434496377245431116940), (+1.22326404910702546039459000657905974, +0.564459063825409121526053066492397358), (+1.61642869446562652939526799815576176, +0.890951511796087664049552095604641970), (+1.92401958335728788933505102105767244, +0.276719156538248855678108249213307092), (+1.65840165646048856497341132433616638, +0.848558381067505319140353136510117456E-1), (+1.33873925959941657597048356118079003, +0.185606714202874700967708534393879152), (+1.78429553968383352180812735501833400, +0.259877733129051621208128342042066387E-1), (+1.02703452020407456390503127644054046, +0.214451234530421735923396267140916513), (+1.11503171284802701156498351765981652, +0.399508504264245137738527124885615340), (+1.93806228179867286339020669047719507, +0.429412757064973614713469207532162641), (+1.35254575727030142637903973160802388, +0.266790741406755818893981027240289140), (+1.59919558735278543701917805956184633, +0.136955716830925338842599995975608116), (+1.03254034291940897661245060665424264, +0.762115014750697857200755520151183867), (+1.67407027680792061882972884027653511, +0.305977646197449272917861444053958773), (+1.48238941919379521469017264815158797, +0.753196776728598657412803328116483621E-1), (+1.93662021725149865909643822648822893, +0.864888303958037143638022768049210537), (+1.61725968691786644765422302951392593, +0.907014401464751299375537991311874084E-1), (+1.05063867525767378153910928252438808, +0.649363538361850795257725811197558943), (+1.98533036949494937550634839354653341, +0.978428058178066307446772062550420813), (+1.43714084409112203279788023573729612, +0.637757583286946612679153369679664963), (+1.91403237673997047632077133143267740, +0.616919198641998375918392304018694755), (+1.13329063162064974134885881075851992, +0.846518855994519113645813225529961086), (+1.00479156354850475841820772609195496, +0.122895775654529913870536725282284984), (+1.64385360538846120778763371591560758, +0.995239611852543829810650029924462421), (+1.08766580748102033406707273424502628, +0.890103864024259585038611209478764282), (+1.92133291410490415428418105982592218, +0.561269031715289347609893866967845534E-1), (+1.61891225685575930813535588446419178, +0.424970313176730148579150264915185837), (+1.80791110659805028715921382884441128, +0.967975858784729728966931881630903045), (+1.87608402922451302730327425492683148, +0.817129613679891827635456092094431423), (+1.45435753653294623492321352590105111, +0.681034769525937230062964162455206984), (+1.44780987562304920088142291853794576, +0.565576000979829133158014378906009142), (+1.71222016610105896991702556597214169, +0.605940018835466097287124501513362793), (+1.54814389349364767745342176745729260, +0.189638170032812310705662369756049153E-1), (+1.07054698910666859303943907836059991, +0.360236590152514166718880840093323487), (+1.81964862036214517204860460394616884, +0.443741206232616007626255208335426926), (+1.66812898892942097286750164060050989, +0.822557584346872807752851936907397864), (+1.09433651356005915609071078832634346, +0.561312201660414772209574130864756084), (+1.25944104414694389560555393507948546, +0.710777522662938610185794897810214273), (+1.78906839374144669764836525922724944, +0.676304452469370657726635178359594345), (+1.34594368299975027781345239741949326, +0.911445430381375978491657312093995336), (+1.41130999676802300161802174511898786, +0.661117345392313074227712160547331005), (+1.84236109407886189365248357986620818, +0.525253393023168124461965697496221823), (+1.88545742853494169904860433721120015, +0.514842645339052866159290972679898462), (+1.73447550890867852221161469818345986, +0.170566840956571068815231654573747698), (+1.70988252537815722873659316711214249, +0.758024107712617815123125889830990888), (+1.36388359463940171013270853245699958, +0.126007873095696873953235240526686163), (+1.89582512550557021719672123961641524, +0.362155324990858866177609462099864241), (+1.21739341858653554975110942094918512, +0.204765127773809416474390220318329097), (+1.48114336956753717740110151454521096, +0.451332792474770369511836921261264526), (+1.52622729532604134304387644207158753, +0.223067471501861935203775437088732794E-1), (+1.18957718728010159265323174832067301, +0.233625049356518471634671485437626160), (+1.66754687939022315462604812272144185, +0.372793971367329210286281832231092452)

143

144adat = getFFTR(getFFTF(data)) / size(data)

145adat

146(+1.48912045318769675155132589246311138, +0.914307180470642470374057901579121570), (+1.06780130203332572381004744614804589, +0.287195640566712012176812545271084713), (+1.95078762934547436440589617404764236, +0.353016097909431550029843777591644468), (+1.89391095336954232005780173177661763, +0.835847469201370681093420897266977558), (+1.19473482509093926218753349250064251, +0.707963309115863378785890868333808355), (+1.19995921255796866980450645612351529, +0.269385685353125133085763591663619269), (+1.47835649561370204716972628397914750, +0.710888373492738406877804566841618761), (+1.16842363745638728893249175968680315, +0.996768559415545672804870508827342237), (+1.53832350339495799859929124047515864, +0.967505217332575329093715940365578593), (+1.75643706011308950486474648193471474, +0.495096105149147844491019168633713414E-1), (+1.27642218499052027671376701457923788, +0.337099889043289042093571065706280827), (+1.87458930242951756406303931072893910, +0.450171938699994300834295678555055118), (+1.23650833534106086733962618997778627, +0.284783162243330904888146312077920395E-1), (+1.06002156190256418074375401234385330, +0.264033027667058287771230900202623671), (+1.24208135925346567268430952831281444, +0.594237234834116822525772044342633044), (+1.84629298154802038380631437110517748, +0.808950767742248492806966410808595436), (+1.28101381891181917214220416967216504, +0.671772131477051665097962783143574658E-1), (+1.51608214693430740454173463534331656, +0.328798315921688663958753149688869180E-1), (+1.50026169956443829908007063430204326, +0.750515545346938125569652110708923692), (+1.50248358930734418997845964342914746, +0.491264222015660866610450713227409789E-1), (+1.20550150856410990993938244185823650, +0.199477467182020520265323562815405722), (+1.67582629910434113851807902073754846, +0.962844817896523712045597921246430439), (+1.87340473466396799961259185424063722, +0.234945333069173434496377245431117205), (+1.22326404910702546039459000657905936, +0.564459063825409121526053066492397550), (+1.61642869446562652939526799815576118, +0.890951511796087664049552095604641778), (+1.92401958335728788933505102105767244, +0.276719156538248855678108249213307044), (+1.65840165646048856497341132433616696, +0.848558381067505319140353136510119021E-1), (+1.33873925959941657597048356118078964, +0.185606714202874700967708534393879417), (+1.78429553968383352180812735501833419, +0.259877733129051621208128342042070179E-1), (+1.02703452020407456390503127644054026, +0.214451234530421735923396267140916489), (+1.11503171284802701156498351765981594, +0.399508504264245137738527124885615292), (+1.93806228179867286339020669047719526, +0.429412757064973614713469207532162978), (+1.35254575727030142637903973160802349, +0.266790741406755818893981027240289236), (+1.59919558735278543701917805956184652, +0.136955716830925338842599995975608261), (+1.03254034291940897661245060665424245, +0.762115014750697857200755520151183867), (+1.67407027680792061882972884027653530, +0.305977646197449272917861444053958725), (+1.48238941919379521469017264815158797, +0.753196776728598657412803328116485427E-1), (+1.93662021725149865909643822648822989, +0.864888303958037143638022768049211211), (+1.61725968691786644765422302951392554, +0.907014401464751299375537991311874325E-1), (+1.05063867525767378153910928252438847, +0.649363538361850795257725811197558943), (+1.98533036949494937550634839354653302, +0.978428058178066307446772062550420524), (+1.43714084409112203279788023573729632, +0.637757583286946612679153369679664770), (+1.91403237673997047632077133143267740, +0.616919198641998375918392304018694852), (+1.13329063162064974134885881075851992, +0.846518855994519113645813225529961182), (+1.00479156354850475841820772609195419, +0.122895775654529913870536725282284948), (+1.64385360538846120778763371591560758, +0.995239611852543829810650029924462421), (+1.08766580748102033406707273424502667, +0.890103864024259585038611209478764571), (+1.92133291410490415428418105982592198, +0.561269031715289347609893866967846377E-1), (+1.61891225685575930813535588446419236, +0.424970313176730148579150264915185885), (+1.80791110659805028715921382884441128, +0.967975858784729728966931881630903237), (+1.87608402922451302730327425492683090, +0.817129613679891827635456092094431519), (+1.45435753653294623492321352590105092, +0.681034769525937230062964162455206887), (+1.44780987562304920088142291853794499, +0.565576000979829133158014378906009335), (+1.71222016610105896991702556597214188, +0.605940018835466097287124501513362985), (+1.54814389349364767745342176745729337, +0.189638170032812310705662369756051862E-1), (+1.07054698910666859303943907836060049, +0.360236590152514166718880840093323872), (+1.81964862036214517204860460394616884, +0.443741206232616007626255208335427167), (+1.66812898892942097286750164060051066, +0.822557584346872807752851936907397960), (+1.09433651356005915609071078832634365, +0.561312201660414772209574130864756276), (+1.25944104414694389560555393507948566, +0.710777522662938610185794897810214562), (+1.78906839374144669764836525922724925, +0.676304452469370657726635178359594441), (+1.34594368299975027781345239741949326, +0.911445430381375978491657312093995432), (+1.41130999676802300161802174511898767, +0.661117345392313074227712160547331198), (+1.84236109407886189365248357986620875, +0.525253393023168124461965697496222015), (+1.88545742853494169904860433721120034, +0.514842645339052866159290972679898462), (+1.73447550890867852221161469818346005, +0.170566840956571068815231654573747867), (+1.70988252537815722873659316711214230, +0.758024107712617815123125889830991177), (+1.36388359463940171013270853245699900, +0.126007873095696873953235240526686042), (+1.89582512550557021719672123961641543, +0.362155324990858866177609462099864530), (+1.21739341858653554975110942094918531, +0.204765127773809416474390220318329194), (+1.48114336956753717740110151454521076, +0.451332792474770369511836921261264670), (+1.52622729532604134304387644207158734, +0.223067471501861935203775437088730206E-1), (+1.18957718728010159265323174832067263, +0.233625049356518471634671485437626112), (+1.66754687939022315462604812272144243, +0.372793971367329210286281832231092500)

147reltol = sqrt(epsilon(1._TKG))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, adat, reltol = reltol)

151T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

152call setAsserted(all(isClose(data, adat, reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+87

157data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

158data

159+1.28859758, +1.38612676, +1.04306853, +1.53073406, +1.06976271, +1.19684815, +1.87941813, +1.18565953, +1.61693490, +1.10703564, +1.84729004, +1.71233940, +1.64521849, +1.01942027, +1.64118743, +1.86077607, +1.02312875, +1.64253402, +1.07063317, +1.58027530, +1.32046986, +1.71765566, +1.66499734, +1.93933010, +1.43396330, +1.97124529, +1.04575849, +1.06829548, +1.80092311, +1.30179751, +1.12883043, +1.99022293, +1.66539276, +1.84058118, +1.50583029, +1.05962038, +1.66225863, +1.97188675, +1.26406705, +1.83875251, +1.89514351, +1.04933882, +1.01217628, +1.22790074, +1.96126318, +1.24534893, +1.86127806, +1.06180692, +1.56912422, +1.60556912, +1.62249565, +1.02467895, +1.59700656, +1.41459394, +1.12093174, +1.05233014, +1.65797472, +1.32288802, +1.58848238, +1.30081534, +1.43414867, +1.40514684, +1.49105501, +1.91265917, +1.17572713, +1.13299036, +1.19111037, +1.35053265, +1.41320801, +1.92588222, +1.98531699, +1.15885806, +1.93627024, +1.92630744, +1.59611261, +1.55486524, +1.75233543, +1.50962996, +1.61162901, +1.05960107, +1.49717188, +1.41889691, +1.25927746, +1.76342893, +1.87624872, +1.39498973, +1.48070693

160

161adat = getFFTR(getFFTF(data)) / size(data)

162adat

163+1.28859782, +1.38612711, +1.04306877, +1.53073430, +1.06976223, +1.19684827, +1.87941790, +1.18566000, +1.61693454, +1.10703599, +1.84728897, +1.71233904, +1.64521861, +1.01942062, +1.64118695, +1.86077595, +1.02312791, +1.64253354, +1.07063377, +1.58027530, +1.32047009, +1.71765518, +1.66499674, +1.93932915, +1.43396354, +1.97124529, +1.04575920, +1.06829572, +1.80092227, +1.30179703, +1.12883091, +1.99022257, +1.66539180, +1.84057999, +1.50582957, +1.05962014, +1.66225886, +1.97188747, +1.26406682, +1.83875120, +1.89514112, +1.04933941, +1.01217830, +1.22790492, +1.96126270, +1.24534953, +1.86127937, +1.06181109, +1.56912386, +1.60556817, +1.62249315, +1.02467930, +1.59700680, +1.41459525, +1.12093198, +1.05232990, +1.65797281, +1.32288778, +1.58848226, +1.30081546, +1.43414903, +1.40514612, +1.49105394, +1.91265869, +1.17572773, +1.13299084, +1.19111085, +1.35053241, +1.41320753, +1.92588198, +1.98531687, +1.15885830, +1.93627012, +1.92630649, +1.59611213, +1.55486548, +1.75233543, +1.50962985, +1.61162913, +1.05960083, +1.49717152, +1.41889703, +1.25927746, +1.76342881, +1.87624872, +1.39498913, +1.48070693

164reltol = sqrt(epsilon(1._TKG))

165reltol

166+0.345266977E-3

167isClose(data, adat, reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, adat, reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+61

174data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

175data

176+1.5637680782348999, +1.6105991323650617, +1.0614959053923299, +1.0959802782507500, +1.4637809064716762, +1.5932584458275736, +1.6297705816857406, +1.8723070642812409, +1.8045262549884988, +1.0394373372156547, +1.4292357334491967, +1.5612304516541267, +1.0598343401289918, +1.5045157884001310, +1.6811986587509753, +1.9425334619435355, +1.5729489601448390, +1.4034418086008267, +1.7109057241037933, +1.3937010147258739, +1.5532264328718126, +1.3333217390390504, +1.9972117372341744, +1.3334100916457958, +1.2172449569945893, +1.8130378464375656, +1.7020311810291178, +1.5149114078139361, +1.3704722803867824, +1.5004580657838842, +1.3824971082196764, +1.6630367527783130, +1.1680666669582749, +1.9158222535009712, +1.6457615944566466, +1.6702560073460799, +1.0531117384218243, +1.1756708592094134, +1.5091666849381558, +1.6402452716601332, +1.5588041887753565, +1.5702412682203655, +1.0325369190356102, +1.8498120099128399, +1.3184644722270782, +1.3776238096369062, +1.6828596415816734, +1.9673625818567364, +1.9171072559253086, +1.9564622404888392, +1.5373250864828214, +1.5144316172317409, +1.1309057762552874, +1.5300226744325203, +1.0290047693202831, +1.2673545558223531, +1.2846936117657832, +1.7374150917322879, +1.8824894059577240, +1.1539140563914225, +1.8751368921805107

177

178adat = getFFTR(getFFTF(data)) / size(data)

179adat

180+1.5637680782348995, +1.6105991323650615, +1.0614959053923299, +1.0959802782507495, +1.4637809064716758, +1.5932584458275729, +1.6297705816857406, +1.8723070642812412, +1.8045262549884988, +1.0394373372156545, +1.4292357334491959, +1.5612304516541260, +1.0598343401289925, +1.5045157884001321, +1.6811986587509749, +1.9425334619435353, +1.5729489601448385, +1.4034418086008267, +1.7109057241037917, +1.3937010147258737, +1.5532264328718131, +1.3333217390390497, +1.9972117372341718, +1.3334100916457952, +1.2172449569945889, +1.8130378464375658, +1.7020311810291180, +1.5149114078139378, +1.3704722803867810, +1.5004580657838833, +1.3824971082196733, +1.6630367527783130, +1.1680666669582722, +1.9158222535009735, +1.6457615944566457, +1.6702560073460808, +1.0531117384218247, +1.1756708592094134, +1.5091666849381538, +1.6402452716601303, +1.5588041887753554, +1.5702412682203661, +1.0325369190356117, +1.8498120099128381, +1.3184644722270777, +1.3776238096369064, +1.6828596415816734, +1.9673625818567351, +1.9171072559253088, +1.9564622404888383, +1.5373250864828227, +1.5144316172317409, +1.1309057762552870, +1.5300226744325196, +1.0290047693202820, +1.2673545558223531, +1.2846936117657815, +1.7374150917322877, +1.8824894059577229, +1.1539140563914234, +1.8751368921805112

181reltol = sqrt(epsilon(1._TKG))

182reltol

183+0.14901161193847656E-7

184isClose(data, adat, reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, adat, reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+79

191data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

192data

193+1.72971965319758140250520553724052120, +1.09312121732797875226010116808997575, +1.39257035212326216783144931103927782, +1.27230036611060972264283513399401400, +1.53135278943274923237221032797664818, +1.09420366676385427838098884120845276, +1.33388182442882334197204586397931324, +1.51639941339791396618594152911375979, +1.32849395818796429865425176998448365, +1.76687256529013149317309053538335108, +1.96166360281666101988547493759628093, +1.74136581394056257575552523416662361, +1.16371829247077716414012579580090536, +1.73433611106118415683510184111262626, +1.33200505419590652483460880171649224, +1.61883564672413345762167900425461382, +1.78686263707461623217450496742154331, +1.57755948384883621241059837406913813, +1.50418343839008012717749287008717274, +1.48059782249482550008633182123007905, +1.42835679671624473206160399279826463, +1.05893775632265995162027133946048216, +1.49833600684583361364344554994587950, +1.51658144180223095451265540230974607, +1.12149311442391615106215079499117567, +1.52482179751016933798373707599051153, +1.91742948974920485576805742705199154, +1.40401967669918874213643510955516426, +1.42986681170460009786489033501871019, +1.39635973627407361853508998403112483, +1.68064111411329886693609189437254703, +1.60686115523216979535532014233856153, +1.58509706675609152280784212803872083, +1.09910075544843873815530401953156325, +1.76174646082560256110224124076454383, +1.12208548782730836389423969531829167, +1.34752221357875448907755739134776481, +1.67505103682600551169120085463733264, +1.48925111241276242896999005901975505, +1.41926574245703172882665719023086954, +1.83916248442370959965701214598765120, +1.72900073788671435842379935696909844, +1.46929999204343018830213893098572865, +1.93477109999153321274548679996399895, +1.10218715577625496364827236285226026, +1.56835198735267852351753480074338004, +1.86911568666456278405870323532024560, +1.97416806929323202630674801953542111, +1.10602173050676075449477260485640969, +1.05218111428812115402615698228561593, +1.35004218416802204181780909642227429, +1.84735581719467825322591163382226418, +1.25699468083592004014593673734893417, +1.81326404847938337424869716369989047, +1.72719938444865773477645973433144501, +1.60913614071770816255148042486033977, +1.01649864088739036359633669143098396, +1.47287530407536437599856931288983006, +1.18845647996863437908921520817466772, +1.60513604583186134536905548984769334, +1.81885983637481864007107087418920948, +1.18649202875048940967521945936018570, +1.42621663009985578196965008831321021, +1.77566320726726271448707123879521145, +1.87424689241410600939830130034725345, +1.98661583418954280678514434824065631, +1.54534481126055559977857649636041472, +1.25380540021808851512193837886418170, +1.99390068993928752007406517577335377, +1.25393077295455236314715338681036112, +1.71150519825939133831930492756467371, +1.67260187592767519582130093892073225, +1.53448729164748719772511192015851678, +1.14341855342136723207092810121639109, +1.49263168076400171874298841469171624, +1.97319920498053073141939621004842053, +1.64923881871851317076999228063347597, +1.50939997281474299792245181328655618, +1.82052038815359191280530105622653715

194

195adat = getFFTR(getFFTF(data)) / size(data)

196adat

197+1.72971965319758140250520553724052217, +1.09312121732797875226010116808997671, +1.39257035212326216783144931103927917, +1.27230036611060972264283513399401612, +1.53135278943274923237221032797664703, +1.09420366676385427838098884120845584, +1.33388182442882334197204586397931439, +1.51639941339791396618594152911375767, +1.32849395818796429865425176998448789, +1.76687256529013149317309053538334954, +1.96166360281666101988547493759627747, +1.74136581394056257575552523416661976, +1.16371829247077716414012579580091441, +1.73433611106118415683510184111261914, +1.33200505419590652483460880171649782, +1.61883564672413345762167900425461189, +1.78686263707461623217450496742153792, +1.57755948384883621241059837406913851, +1.50418343839008012717749287008717332, +1.48059782249482550008633182123007886, +1.42835679671624473206160399279826271, +1.05893775632265995162027133946049506, +1.49833600684583361364344554994587450, +1.51658144180223095451265540230974221, +1.12149311442391615106215079499118781, +1.52482179751016933798373707599051191, +1.91742948974920485576805742705197574, +1.40401967669918874213643510955517043, +1.42986681170460009786489033501871077, +1.39635973627407361853508998403113022, +1.68064111411329886693609189437254010, +1.60686115523216979535532014233856210, +1.58509706675609152280784212803871236, +1.09910075544843873815530401953158424, +1.76174646082560256110224124076452014, +1.12208548782730836389423969531830573, +1.34752221357875448907755739134776616, +1.67505103682600551169120085463732224, +1.48925111241276242896999005901975775, +1.41926574245703172882665719023088168, +1.83916248442370959965701214598764061, +1.72900073788671435842379935696909363, +1.46929999204343018830213893098573982, +1.93477109999153321274548679996397275, +1.10218715577625496364827236285228434, +1.56835198735267852351753480074337369, +1.86911568666456278405870323532023789, +1.97416806929323202630674801953539954, +1.10602173050676075449477260485642818, +1.05218111428812115402615698228562768, +1.35004218416802204181780909642227930, +1.84735581719467825322591163382224704, +1.25699468083592004014593673734895093, +1.81326404847938337424869716369987891, +1.72719938444865773477645973433144250, +1.60913614071770816255148042486033283, +1.01649864088739036359633669143100013, +1.47287530407536437599856931288982275, +1.18845647996863437908921520817467832, +1.60513604583186134536905548984769026, +1.81885983637481864007107087418919985, +1.18649202875048940967521945936019668, +1.42621663009985578196965008831321272, +1.77566320726726271448707123879520721, +1.87424689241410600939830130034725075, +1.98661583418954280678514434824064880, +1.54534481126055559977857649636041645, +1.25380540021808851512193837886418979, +1.99390068993928752007406517577334491, +1.25393077295455236314715338681036979, +1.71150519825939133831930492756466851, +1.67260187592767519582130093892073244, +1.53448729164748719772511192015851621, +1.14341855342136723207092810121639533, +1.49263168076400171874298841469171701, +1.97319920498053073141939621004841841, +1.64923881871851317076999228063347789, +1.50939997281474299792245181328655734, +1.82052038815359191280530105622653638

198reltol = sqrt(epsilon(1._TKG))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, adat, reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, adat, reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+24

208data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

209data

210(+1.60899699, +0.781319201), (+1.98622537, +0.648481250E-1), (+1.80280042, +0.183516085), (+1.81077027, +0.645927727), (+1.52667618, +0.863293171), (+1.07563293, +0.745814800), (+1.83485663, +0.955190659), (+1.50166130, +0.492416263), (+1.12562275, +0.745653152), (+1.16110861, +0.337773979), (+1.94052649, +0.845683694), (+1.41622686, +0.296028852), (+1.92734134, +0.948393285), (+1.05131054, +0.823030651), (+1.60849500, +0.509418726), (+1.56059813, +0.920987666), (+1.17199254, +0.323617578), (+1.48796558, +0.372072339), (+1.30124760, +0.370134890), (+1.60038018, +0.875325263), (+1.63406432, +0.273431480), (+1.15742898, +0.919075489), (+1.76609397, +0.484680295), (+1.03930151, +0.799854994E-1)

211

212adat = getFFTR(getFFTF(data)) / size(data)

213adat

214(+1.60899687, +0.781319201), (+1.98622549, +0.648481846E-1), (+1.80280054, +0.183516070), (+1.81077039, +0.645927727), (+1.52667618, +0.863293231), (+1.07563293, +0.745814800), (+1.83485687, +0.955190599), (+1.50166118, +0.492416292), (+1.12562263, +0.745653212), (+1.16110861, +0.337774128), (+1.94052684, +0.845683753), (+1.41622674, +0.296028852), (+1.92734134, +0.948393285), (+1.05131066, +0.823030651), (+1.60849512, +0.509418786), (+1.56059802, +0.920987785), (+1.17199266, +0.323617607), (+1.48796558, +0.372072369), (+1.30124772, +0.370134830), (+1.60038006, +0.875325263), (+1.63406420, +0.273431540), (+1.15742898, +0.919075549), (+1.76609433, +0.484680295), (+1.03930140, +0.799855515E-1)

215reltol = sqrt(epsilon(1._TKG))

216reltol

217+0.345266977E-3

218isClose(data, adat, reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, adat, reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+49

225data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

226data

227(+1.2167087883612329, +0.58740520434406029E-2), (+1.6991944173446845, +0.92048552610652112), (+1.5228510887438076, +0.72598159259690997), (+1.1704113751279190, +0.40955957699751577), (+1.2515718136004703, +0.40293957769682187), (+1.2456536189938463, +0.62458700467487027), (+1.3077678455883390, +0.91384048566873111), (+1.4782607496864104, +0.83431027974597305), (+1.1841219997854062, +0.60066538025269445), (+1.6854636550288178, +0.61374615969949220), (+1.5368804485755017, +0.41772609818243422), (+1.7718542010539198, +0.50029959311987882), (+1.1310962444490706, +0.72591135876118407), (+1.9882781685668807, +0.25385451627552624), (+1.6707970275856270, +0.88404067773533335), (+1.6142760403175012, +0.58421169740315970E-1), (+1.6380459396880096, +0.63141843176136581E-2), (+1.0222919454618287, +0.23693379021598804), (+1.6113077904411686, +0.32705328225518704), (+1.1136835624106891, +0.97333632629402600), (+1.7320437092789498, +0.96006922035619668E-2), (+1.9258654530115846, +0.51783034198409050), (+1.4963289273001157, +0.13957243675161601), (+1.1259047974615370, +0.66407003438227508), (+1.0217348706446483, +0.14374202997944030), (+1.8895218069813593, +0.44727023856269921), (+1.0053796639253116, +0.39821991464237994), (+1.2345614011958195, +0.37343962998163305), (+1.0658864185738408, +0.45136606293303438), (+1.0445050681066945, +0.38258797660321775), (+1.7389073288139887, +0.93065063296088679), (+1.6356602413432724, +0.11610919279704146), (+1.2916199030869722, +0.46786680399873659), (+1.2125779459041726, +0.22307912084904435), (+1.7254529407745138, +0.75798497158529687), (+1.5291317670770748, +0.96639166282749445), (+1.2535911727447151, +0.45731615796338443E-1), (+1.1707843755898053, +0.13140911057179594), (+1.9977176713095548, +0.81304490837466881), (+1.8783605699586676, +0.44787009284405310), (+1.0786571911687188, +0.83644012414568591), (+1.2503221805112503, +0.53271278829299185), (+1.9697050271792480, +0.37627896264245875), (+1.0116833084016092, +0.19943473811008550), (+1.4301606199331531, +0.15810731464390093), (+1.9354616886548377, +0.18254445411394693), (+1.2282993046383002, +0.53816224165114868), (+1.5037241994525075, +0.82650808234516759E-2), (+1.7171715058613093, +0.26365584326657787)

228

229adat = getFFTR(getFFTF(data)) / size(data)

230adat

231(+1.2167087883612333, +0.58740520434406480E-2), (+1.6991944173446847, +0.92048552610652135), (+1.5228510887438078, +0.72598159259691009), (+1.1704113751279190, +0.40955957699751566), (+1.2515718136004705, +0.40293957769682182), (+1.2456536189938465, +0.62458700467487016), (+1.3077678455883395, +0.91384048566873111), (+1.4782607496864104, +0.83431027974597305), (+1.1841219997854062, +0.60066538025269456), (+1.6854636550288180, +0.61374615969949209), (+1.5368804485755014, +0.41772609818243422), (+1.7718542010539198, +0.50029959311987882), (+1.1310962444490704, +0.72591135876118418), (+1.9882781685668811, +0.25385451627552658), (+1.6707970275856272, +0.88404067773533324), (+1.6142760403175014, +0.58421169740316144E-1), (+1.6380459396880096, +0.63141843176136693E-2), (+1.0222919454618284, +0.23693379021598793), (+1.6113077904411686, +0.32705328225518704), (+1.1136835624106889, +0.97333632629402578), (+1.7320437092789509, +0.96006922035621282E-2), (+1.9258654530115846, +0.51783034198409039), (+1.4963289273001159, +0.13957243675161607), (+1.1259047974615373, +0.66407003438227474), (+1.0217348706446481, +0.14374202997944024), (+1.8895218069813593, +0.44727023856269910), (+1.0053796639253116, +0.39821991464238005), (+1.2345614011958190, +0.37343962998163305), (+1.0658864185738408, +0.45136606293303438), (+1.0445050681066945, +0.38258797660321786), (+1.7389073288139891, +0.93065063296088657), (+1.6356602413432721, +0.11610919279704122), (+1.2916199030869719, +0.46786680399873648), (+1.2125779459041723, +0.22307912084904430), (+1.7254529407745136, +0.75798497158529710), (+1.5291317670770750, +0.96639166282749456), (+1.2535911727447153, +0.45731615796338575E-1), (+1.1707843755898055, +0.13140911057179588), (+1.9977176713095544, +0.81304490837466870), (+1.8783605699586674, +0.44787009284405283), (+1.0786571911687188, +0.83644012414568591), (+1.2503221805112512, +0.53271278829299207), (+1.9697050271792480, +0.37627896264245864), (+1.0116833084016095, +0.19943473811008555), (+1.4301606199331534, +0.15810731464390093), (+1.9354616886548379, +0.18254445411394687), (+1.2282993046383002, +0.53816224165114868), (+1.5037241994525072, +0.82650808234518390E-2), (+1.7171715058613095, +0.26365584326657787)

232reltol = sqrt(epsilon(1._TKG))

233reltol

234+0.14901161193847656E-7

235isClose(data, adat, reltol = reltol)

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, adat, reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+75

242data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

243data

244(+1.10325901122146591941002522271914517, +0.628572111800637087405681162292704684), (+1.40888053254070897107032872265658089, +0.941940739757385879699147166469170958), (+1.52697764130669070984969474801809139, +0.689312666710291162608875845905691995), (+1.54089959633509018416744144937975368, +0.157046613784003563744839240339103568), (+1.73898330707968991902566182479701871, +0.171611712488166216324853008282765408), (+1.76909505317342333955699622524392875, +0.842509642815216507565629399338676793E-1), (+1.44477923703223199176772335208631381, +0.543759728574361897566523293317861978), (+1.17090912537323494329023442753263725, +0.918821802903794920632864215344045093), (+1.69756776228734046668488318118278018, +0.321649134923910983145311430736935814), (+1.43582657835693200848083061836119300, +0.417970267307033576394838460746332802), (+1.39914223549711418313633560755129071, +0.348309276402594903555279024735655426), (+1.04722319396055132819704719064643254, +0.468771106456342376928029356375482616), (+1.10351984025272766539063688631829806, +0.552817846132866853593282429641647576), (+1.66765711607562257848860349891940694, +0.739967720950595652045777330997494605), (+1.94507858269147309965304024887240903, +0.140234641258383155928137720602883175), (+1.62897614226689313295740212964779340, +0.629120407717157014890346971433752738), (+1.41611839516686597684456158249285166, +0.524433063564801352798463234871129234E-2), (+1.86051975491230541349397935821280254, +0.744393052745837527065440054446588574), (+1.32826190115427936460065305050581651, +0.446458064220070499776648276642819290), (+1.25871750798290853765645981897809338, +0.115499052672130018616647470268942219), (+1.97694067096943091344190123940692028, +0.253793666960503042630564867460187730), (+1.25035241407125508561103929582660017, +0.720319153242530254885473955303553436), (+1.78743148730916170236870808722746433, +0.310786303166137115836702854254330336), (+1.65374372201647250343155523047745818, +0.988732095449591366075537036184616980), (+1.48382094105773048536270045319277424, +0.545880755756007701972259351164561676), (+1.30460860518482814649025078178338466, +0.500252565019285631560792298419161686), (+1.05319731484624218218080048928118960, +0.933559097589179906180300335921735952), (+1.34282613603662939587910975529070252, +0.414230196304123239881435373362616927), (+1.38467349321876747113847294423263972, +0.873128222304963162931300699097856457), (+1.29840301626543853675976529348528346, +0.685753077631685400085925173237417681), (+1.93962250684114722379889554834226013, +0.197343664334252030792879248243561799), (+1.08016670929968699550989427695368956, +0.537449909046139986154031263973402017), (+1.26598089873609197507243109006956776, +0.488899511918383529560167980744502906), (+1.37667820435069917078678207564243572, +0.810961918790482665701986787649095410), (+1.17839736505437809438061325373734967, +0.664745244757688091066158269068118309), (+1.77597936003215300916369614752202477, +0.692798110562405398893621333539219879E-1), (+1.14887599458242242995866126932178597, +0.726905611851114217691573311546799508), (+1.37742022444093615351901190351424079, +0.337558383413529378278643543764336283), (+1.86822982198252301429636291797674875, +0.985428871441450560329526430243347051), (+1.24082950154708227901505374543589300, +0.109269619588895248222717548737438065), (+1.26451277737655523689897841139239776, +0.533369600646553965108194730510319857), (+1.35153308851183641400837302386598166, +0.234659725211052566193260168760951624), (+1.81350181212623253963873694900828141, +0.712072364198021495715016881777431907), (+1.11259904848425343252653222367801946, +0.864611046899729445453694600341831784), (+1.71141993346257903751369981453249640, +0.938111695860731158131580369987051779), (+1.84960982120926968034735981841322134, +0.985199023994501372122790516726237682), (+1.19794487373418089289660915728670865, +0.754051310080566036554496648710982101), (+1.32468184972064835261678009327192924, +0.591070206861393936662324211756886055), (+1.54059023686850353571905132809639101, +0.883711557124777379550953477543974581), (+1.07238312087137261954466204042662660, +0.901245929299198197084123798702917545), (+1.57538192988236174589193922555905852, +0.485981981571265563729459039467842165), (+1.78784867567342435803407299443656799, +0.365662420381769490915217438882035388), (+1.79342351052476884134473620569261380, +0.121590575853311452042442842226871511), (+1.40984776872940003763766034526865410, +0.189020120557994140923992055205420557E-2), (+1.35775569663235372182261281666554941, +0.924332914353234401563029880560928052), (+1.34583156562659062761134978426545589, +0.955644865266092758717167187730036221), (+1.56038013413248252021751041861559254, +0.682425767081157475892924815680055551), (+1.83192949988812219396702802326629557, +0.457382331108881202975427094590981066), (+1.23954428448462577730219369515709904, +0.846438017493345757749652360185748355E-1), (+1.72251272182557569921936821826519199, +0.291149119087390592825120892768635394), (+1.39320001368216121316457879651294658, +0.193557490248699085645808452695126032), (+1.03809069094351329993822409773159855, +0.909388950984515958637281812744752437), (+1.12804476317427901783830146306758411, +0.279845076924758328848290824954486830E-1), (+1.26017783713878610321580862201681804, +0.801705895227018683196218839832119249), (+1.25118792794055101567452177158797984, +0.930986111224897527984956126355451178), (+1.40564146633878601035240497729012525, +0.292460419032097176495781953455962134), (+1.71544133307455570367952315781998532, +0.873854450174893476714456863255480016), (+1.54247420390031487106544154776587027, +0.367884289448720524880785129694358314), (+1.43188535847695040846764624269434022, +0.520666717170505013442101012278877423), (+1.22968402957813307580901918979465244, +0.405368293830716081065418305128699933), (+1.59108067409245259226988820015898358, +0.296014336261713816875620170534475122), (+1.99901482979028312522114310981365327, +0.990602107228335376210627615360829502), (+1.87628193217620679991119843683547269, +0.695077074311817649108416733547748074), (+1.50581909172690330003157087793073702, +0.332200201977187286407479379498097897), (+1.30665020207562080212816425749770932, +0.941734281920387088703674161362712379)

245

246adat = getFFTR(getFFTF(data)) / size(data)

247adat

248(+1.10325901122146591941002522271914478, +0.628572111800637087405681162292704492), (+1.40888053254070897107032872265658069, +0.941940739757385879699147166469170862), (+1.52697764130669070984969474801809120, +0.689312666710291162608875845905692091), (+1.54089959633509018416744144937975368, +0.157046613784003563744839240339103424), (+1.73898330707968991902566182479701852, +0.171611712488166216324853008282765336), (+1.76909505317342333955699622524392798, +0.842509642815216507565629399338675709E-1), (+1.44477923703223199176772335208631362, +0.543759728574361897566523293317861978), (+1.17090912537323494329023442753263764, +0.918821802903794920632864215344045285), (+1.69756776228734046668488318118277980, +0.321649134923910983145311430736935717), (+1.43582657835693200848083061836119300, +0.417970267307033576394838460746332754), (+1.39914223549711418313633560755129052, +0.348309276402594903555279024735655426), (+1.04722319396055132819704719064643234, +0.468771106456342376928029356375482665), (+1.10351984025272766539063688631829787, +0.552817846132866853593282429641647576), (+1.66765711607562257848860349891940713, +0.739967720950595652045777330997494509), (+1.94507858269147309965304024887240864, +0.140234641258383155928137720602883055), (+1.62897614226689313295740212964779321, +0.629120407717157014890346971433752738), (+1.41611839516686597684456158249285185, +0.524433063564801352798463234871120131E-2), (+1.86051975491230541349397935821280235, +0.744393052745837527065440054446588671), (+1.32826190115427936460065305050581651, +0.446458064220070499776648276642819194), (+1.25871750798290853765645981897809338, +0.115499052672130018616647470268942183), (+1.97694067096943091344190123940691989, +0.253793666960503042630564867460187633), (+1.25035241407125508561103929582660017, +0.720319153242530254885473955303553340), (+1.78743148730916170236870808722746452, +0.310786303166137115836702854254330481), (+1.65374372201647250343155523047745760, +0.988732095449591366075537036184617173), (+1.48382094105773048536270045319277424, +0.545880755756007701972259351164561580), (+1.30460860518482814649025078178338447, +0.500252565019285631560792298419161686), (+1.05319731484624218218080048928118940, +0.933559097589179906180300335921736145), (+1.34282613603662939587910975529070214, +0.414230196304123239881435373362616878), (+1.38467349321876747113847294423263952, +0.873128222304963162931300699097856360), (+1.29840301626543853675976529348528269, +0.685753077631685400085925173237417874), (+1.93962250684114722379889554834225994, +0.197343664334252030792879248243561703), (+1.08016670929968699550989427695368937, +0.537449909046139986154031263973402017), (+1.26598089873609197507243109006956776, +0.488899511918383529560167980744502954), (+1.37667820435069917078678207564243553, +0.810961918790482665701986787649095410), (+1.17839736505437809438061325373734929, +0.664745244757688091066158269068118309), (+1.77597936003215300916369614752202419, +0.692798110562405398893621333539218795E-1), (+1.14887599458242242995866126932178616, +0.726905611851114217691573311546799315), (+1.37742022444093615351901190351424079, +0.337558383413529378278643543764336380), (+1.86822982198252301429636291797674856, +0.985428871441450560329526430243347147), (+1.24082950154708227901505374543589280, +0.109269619588895248222717548737437969), (+1.26451277737655523689897841139239757, +0.533369600646553965108194730510319953), (+1.35153308851183641400837302386598166, +0.234659725211052566193260168760951600), (+1.81350181212623253963873694900828141, +0.712072364198021495715016881777431811), (+1.11259904848425343252653222367801946, +0.864611046899729445453694600341831977), (+1.71141993346257903751369981453249601, +0.938111695860731158131580369987051779), (+1.84960982120926968034735981841322134, +0.985199023994501372122790516726237682), (+1.19794487373418089289660915728670845, +0.754051310080566036554496648710982004), (+1.32468184972064835261678009327192962, +0.591070206861393936662324211756886151), (+1.54059023686850353571905132809639063, +0.883711557124777379550953477543974773), (+1.07238312087137261954466204042662641, +0.901245929299198197084123798702917545), (+1.57538192988236174589193922555905813, +0.485981981571265563729459039467842069), (+1.78784867567342435803407299443656799, +0.365662420381769490915217438882035147), (+1.79342351052476884134473620569261380, +0.121590575853311452042442842226871536), (+1.40984776872940003763766034526865352, +0.189020120557994140923992055205442901E-2), (+1.35775569663235372182261281666554922, +0.924332914353234401563029880560928052), (+1.34583156562659062761134978426545569, +0.955644865266092758717167187730036221), (+1.56038013413248252021751041861559215, +0.682425767081157475892924815680055551), (+1.83192949988812219396702802326629519, +0.457382331108881202975427094590981114), (+1.23954428448462577730219369515709884, +0.846438017493345757749652360185749679E-1), (+1.72251272182557569921936821826519142, +0.291149119087390592825120892768635587), (+1.39320001368216121316457879651294620, +0.193557490248699085645808452695125887), (+1.03809069094351329993822409773159875, +0.909388950984515958637281812744752244), (+1.12804476317427901783830146306758411, +0.279845076924758328848290824954487011E-1), (+1.26017783713878610321580862201681804, +0.801705895227018683196218839832119249), (+1.25118792794055101567452177158797984, +0.930986111224897527984956126355451275), (+1.40564146633878601035240497729012486, +0.292460419032097176495781953455962183), (+1.71544133307455570367952315781998570, +0.873854450174893476714456863255479919), (+1.54247420390031487106544154776587047, +0.367884289448720524880785129694358266), (+1.43188535847695040846764624269434003, +0.520666717170505013442101012278877519), (+1.22968402957813307580901918979465244, +0.405368293830716081065418305128699933), (+1.59108067409245259226988820015898339, +0.296014336261713816875620170534475074), (+1.99901482979028312522114310981365308, +0.990602107228335376210627615360829502), (+1.87628193217620679991119843683547249, +0.695077074311817649108416733547748074), (+1.50581909172690330003157087793073683, +0.332200201977187286407479379498097897), (+1.30665020207562080212816425749770894, +0.941734281920387088703674161362712475)

249reltol = sqrt(epsilon(1._TKG))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, adat, reltol = reltol)

253T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, adat, reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+73

259data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

260data

261+1.50295258, +1.83340001, +1.58064127, +1.32203102, +1.49863935, +1.77912474, +1.22537756, +1.48350000, +1.62798476, +1.84146762, +1.49358249, +1.62715578, +1.22509313, +1.52384353, +1.24761677, +1.34185719, +1.97970128, +1.33645225, +1.83801544, +1.82054603, +1.34024429, +1.89525914, +1.28760409, +1.51993871, +1.81562972, +1.92939091, +1.39882755, +1.01007199, +1.58501720, +1.93543637, +1.49337304, +1.77405167, +1.73076010, +1.70467710, +1.94372582, +1.08968198, +1.87234294, +1.63938963, +1.80557203, +1.89857054, +1.16577005, +1.78864503, +1.12126303, +1.82259095, +1.07791698, +1.09817457, +1.80887246, +1.98705673, +1.71751285, +1.63897777, +1.66123688, +1.48710692, +1.53811049, +1.19848704, +1.56405640, +1.66052890, +1.09690022, +1.81896234, +1.82870531, +1.38696480, +1.99400020, +1.40100789, +1.58098638, +1.15680909, +1.35977864, +1.43287611, +1.55776620, +1.70755935, +1.28133440, +1.66290951, +1.27023375, +1.99927568, +1.78500056

262

263adat = getFFTR(getFFTF(data)) / size(data)

264adat

265+1.50295162, +1.83339870, +1.58064139, +1.32202899, +1.49863899, +1.77912426, +1.22537613, +1.48349905, +1.62798500, +1.84146869, +1.49358165, +1.62715626, +1.22509134, +1.52384460, +1.24761641, +1.34185290, +1.97970748, +1.33644652, +1.83801818, +1.82054853, +1.34024000, +1.89526367, +1.28760016, +1.51993632, +1.81563365, +1.92939341, +1.39882708, +1.01006281, +1.58502090, +1.93544114, +1.49336958, +1.77405095, +1.73076308, +1.70467150, +1.94374084, +1.08966148, +1.87236440, +1.63940203, +1.80556643, +1.89858401, +1.16575408, +1.78865695, +1.12124944, +1.82260430, +1.07790959, +1.09817028, +1.80887449, +1.98706269, +1.71751106, +1.63897872, +1.66123652, +1.48710680, +1.53811097, +1.19848371, +1.56405687, +1.66053271, +1.09689283, +1.81896639, +1.82870591, +1.38696241, +1.99400413, +1.40100574, +1.58098733, +1.15680766, +1.35977829, +1.43287623, +1.55776525, +1.70756030, +1.28133130, +1.66291010, +1.27023184, +1.99927616, +1.78499949

266reltol = sqrt(epsilon(1._TKG))

267reltol

268+0.345266977E-3

269isClose(data, adat, reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, adat, reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+5

276data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

277data

278+1.0792005546000887, +1.4591177792592100, +1.7299610318559013, +1.8023908984606325, +1.3789659092513737

279

280adat = getFFTR(getFFTF(data)) / size(data)

281adat

282+1.0792005546000891, +1.4591177792592103, +1.7299610318559011, +1.8023908984606323, +1.3789659092513737

283reltol = sqrt(epsilon(1._TKG))

284reltol

285+0.14901161193847656E-7

286isClose(data, adat, reltol = reltol)

287T, T, T, T, T

288call setAsserted(all(isClose(data, adat, reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+5

293data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

294data

295+1.08555995468153227247793156641654339, +1.31155814180846668489813313673875719, +1.38358940656297809636481879225923520, +1.71351970907684809274953567007684696, +1.33825501887126465551412853306887280

296

297adat = getFFTR(getFFTF(data)) / size(data)

298adat

299+1.08555995468153227247793156641654319, +1.31155814180846668489813313673875719, +1.38358940656297809636481879225923520, +1.71351970907684809274953567007684696, +1.33825501887126465551412853306887299

300reltol = sqrt(epsilon(1._TKG))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, adat, reltol = reltol)

304T, T, T, T, T

305call setAsserted(all(isClose(data, adat, reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+99

310data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

311data

312(+1.31694508, +0.903946042), (+1.50875759, +0.222328246), (+1.75007343, +0.828871965), (+1.41123414, +0.387415528), (+1.46535707, +0.594951808), (+1.19499230, +0.197930932E-1), (+1.88524199, +0.433143377E-1), (+1.48066044, +0.227895379), (+1.77557158, +0.843648612), (+1.37476897, +0.804986179), (+1.84123087, +0.814057350), (+1.09240627, +0.343487561), (+1.34116697, +0.762439370), (+1.56446099, +0.970182359), (+1.91927481, +0.857348204), (+1.27373004, +0.372163236), (+1.37135828, +0.842142344), (+1.42291689, +0.667247951), (+1.83090830, +0.183605731), (+1.20936716, +0.420320868), (+1.29955220, +0.576464176), (+1.12595260, +0.779557228E-2), (+1.31802487, +0.689143181), (+1.80987930, +0.982651591), (+1.08729756, +0.176301003), (+1.44277334, +0.325315237), (+1.49361336, +0.322377861), (+1.03484595, +0.456396580), (+1.72428036, +0.662941158), (+1.34052694, +0.715299249), (+1.23469687, +0.441401005), (+1.89245629, +0.532110691), (+1.80251265, +0.534281015), (+1.42777348, +0.721016526E-1), (+1.49637318, +0.368840754), (+1.05328894, +0.284248590), (+1.71696448, +0.438177466), (+1.62378216, +0.784775019), (+1.45714831, +0.859800041), (+1.79357159, +0.320494175E-3), (+1.26201725, +0.281390488), (+1.85318780, +0.392797709), (+1.93093181, +0.560620904), (+1.89395475, +0.941352606), (+1.41462338, +0.408348680), (+1.64238381, +0.523840964), (+1.69886231, +0.183183432), (+1.72115397, +0.710336566E-1), (+1.11217678, +0.128029943), (+1.71829391, +0.123657167), (+1.35475230, +0.888582408), (+1.37371051, +0.320030570), (+1.93104112, +0.635000229), (+1.45777178, +0.536307633), (+1.68882513, +0.722427607), (+1.36719966, +0.161772311), (+1.91046476, +0.279044449), (+1.00047934, +0.306614876), (+1.93268931, +0.798748791), (+1.93365479, +0.259615242), (+1.16533303, +0.592379928), (+1.51049399, +0.204013348), (+1.59919477, +0.829524219), (+1.50808430, +0.320537746), (+1.97050858, +0.670723855), (+1.91580951, +0.511941850), (+1.49495387, +0.823789716), (+1.18106604, +0.672772527), (+1.66880870, +0.737026572), (+1.93183589, +0.363815069), (+1.28498697, +0.527105212), (+1.72914863, +0.199671984E-1), (+1.94291711, +0.186816812), (+1.58383524, +0.761869431), (+1.72615051, +0.742989361), (+1.34013653, +0.490677416), (+1.44960809, +0.193169951), (+1.54821181, +0.125572085E-1), (+1.21474910, +0.149870992), (+1.82532763, +0.282638848), (+1.92969823, +0.274369597), (+1.99927199, +0.312767029), (+1.48831248, +0.687382400), (+1.93569672, +0.668970823), (+1.51383591, +0.183766782), (+1.16342258, +0.204560995), (+1.51862729, +0.949044824E-1), (+1.19387817, +0.998463631E-1), (+1.01904774, +0.272634149), (+1.04057336, +0.692615032), (+1.33082986, +0.464883685), (+1.99646127, +0.103279412), (+1.15767133, +0.991213262), (+1.43883204, +0.827043712), (+1.19350636, +0.448978782), (+1.56962156, +0.373420179), (+1.80484414, +0.924156845), (+1.30280328, +0.250476897), (+1.75821161, +0.843410373)

313

314adat = getFFTR(getFFTF(data)) / size(data)

315adat

316(+1.31694520, +0.903945982), (+1.50875783, +0.222328246), (+1.75007355, +0.828871906), (+1.41123474, +0.387415648), (+1.46535730, +0.594951808), (+1.19499266, +0.197932404E-1), (+1.88524234, +0.433144793E-1), (+1.48066080, +0.227895468), (+1.77557182, +0.843648732), (+1.37476921, +0.804986119), (+1.84123075, +0.814057410), (+1.09240639, +0.343487442), (+1.34116697, +0.762439370), (+1.56446111, +0.970182300), (+1.91927516, +0.857348382), (+1.27373028, +0.372163177), (+1.37135899, +0.842142522), (+1.42291725, +0.667248070), (+1.83090878, +0.183605537), (+1.20936775, +0.420320958), (+1.29955232, +0.576464176), (+1.12595272, +0.779553596E-2), (+1.31802511, +0.689143181), (+1.80987930, +0.982651353), (+1.08729756, +0.176301077), (+1.44277370, +0.325315267), (+1.49361324, +0.322377861), (+1.03484619, +0.456396729), (+1.72428071, +0.662941217), (+1.34052718, +0.715299308), (+1.23469734, +0.441401094), (+1.89245653, +0.532110751), (+1.80251253, +0.534281015), (+1.42777371, +0.721016973E-1), (+1.49637330, +0.368840814), (+1.05328882, +0.284248620), (+1.71696484, +0.438177466), (+1.62378240, +0.784774840), (+1.45714891, +0.859800100), (+1.79357183, +0.320627238E-3), (+1.26201761, +0.281390578), (+1.85318816, +0.392797679), (+1.93093204, +0.560621202), (+1.89395475, +0.941352606), (+1.41462326, +0.408348769), (+1.64238393, +0.523840845), (+1.69886243, +0.183183521), (+1.72115445, +0.710336715E-1), (+1.11217666, +0.128029898), (+1.71829450, +0.123657346), (+1.35475266, +0.888582468), (+1.37371087, +0.320030481), (+1.93104172, +0.635000288), (+1.45777166, +0.536307693), (+1.68882549, +0.722427547), (+1.36719978, +0.161772355), (+1.91046476, +0.279044479), (+1.00047946, +0.306614935), (+1.93268979, +0.798748732), (+1.93365443, +0.259615183), (+1.16533351, +0.592380047), (+1.51049471, +0.204013452), (+1.59919477, +0.829524279), (+1.50808465, +0.320537746), (+1.97050893, +0.670723736), (+1.91580951, +0.511941791), (+1.49495399, +0.823789656), (+1.18106639, +0.672772467), (+1.66880858, +0.737026572), (+1.93183649, +0.363815278), (+1.28498733, +0.527105272), (+1.72914875, +0.199674163E-1), (+1.94291735, +0.186816901), (+1.58383512, +0.761869490), (+1.72615099, +0.742989361), (+1.34013677, +0.490677506), (+1.44960821, +0.193170011), (+1.54821205, +0.125572896E-1), (+1.21474922, +0.149871051), (+1.82532787, +0.282638967), (+1.92969847, +0.274369687), (+1.99927199, +0.312766910), (+1.48831320, +0.687382400), (+1.93569744, +0.668970883), (+1.51383603, +0.183766723), (+1.16342318, +0.204561174), (+1.51862729, +0.949044302E-1), (+1.19387805, +0.998462886E-1), (+1.01904786, +0.272634119), (+1.04057348, +0.692614913), (+1.33083010, +0.464883745), (+1.99646163, +0.103279501), (+1.15767145, +0.991213143), (+1.43883240, +0.827043831), (+1.19350708, +0.448978961), (+1.56962168, +0.373420179), (+1.80484474, +0.924156964), (+1.30280364, +0.250476986), (+1.75821137, +0.843410313)

317reltol = sqrt(epsilon(1._TKG))

318reltol

319+0.345266977E-3

320isClose(data, adat, reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, adat, reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+100

327data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

328data

329(+1.5019857032984378, +0.16111036825601954), (+1.6775075177677052, +0.41271279713563924E-1), (+1.9618042815197962, +0.31163576728909892), (+1.4409941035752241, +0.39632393435528002), (+1.5755553898187946, +0.63793967660307160), (+1.9665943186874242, +0.66632024538880985), (+1.1670264656403531, +0.14002137980123619E-1), (+1.1069109991260793, +0.89985074088651718), (+1.4642076358035421, +0.91947586258458291), (+1.7017292514076039, +0.67221523467457456), (+1.3505446357193929, +0.42880065392576006), (+1.4371100993605932, +0.38511587248515244), (+1.1578045843773586, +0.72372456547642749), (+1.4788391260496594, +0.94360172756093386), (+1.5424460738138528, +0.26027516969416153), (+1.7178303591160315, +0.35458561555591395), (+1.8484004640711902, +0.75018149884742302), (+1.5277313612534282, +0.55425916813761633), (+1.9760780654156203, +0.29977926314061254), (+1.4195758020148475, +0.80822761531820841), (+1.6914324273071291, +0.66100322643333209E-2), (+1.3145766495964586, +0.95728320337143880), (+1.6010685111354490, +0.29365023958192682), (+1.5097994019176928, +0.72284328411660492), (+1.2566451641223124, +0.72327404776017479), (+1.3472625283165749, +0.30499860449770100), (+1.3790177514292465, +0.44825426609542474), (+1.7523640460057737, +0.31841678446966060), (+1.5703844984760198, +0.52548045206495297), (+1.2032223559783739, +0.91782294413784504), (+1.1501950288022351, +0.72923829983788668), (+1.0631420516962899, +0.83317916240009915), (+1.8506533938305081, +0.33238828995918712), (+1.1475260886419005, +0.60369042504404014), (+1.7121114223625518, +0.71934875374421026), (+1.5857316757481863, +0.93257131150376260), (+1.3247907132350729, +0.37363624880374535), (+1.1675367036342195, +0.72640128474529697), (+1.2618306207230292, +0.38754828431025945), (+1.9103591032597933, +0.30667162512795432), (+1.0693249001488749, +0.10747628570787715), (+1.9230469795395995, +0.61790567238822780), (+1.0020414401212312, +0.52188190419192304), (+1.1556931588920980, +0.12280152321092608), (+1.3988328270983805, +0.50228216478500842E-1), (+1.0916756877968354, +0.20793359400863898), (+1.8669092829224123, +0.95936422675018262), (+1.0931100155610953, +0.93167518897909329), (+1.9293689565237977, +0.15507290821847974), (+1.0538731948594260, +0.58085968604167082), (+1.7111899070897088, +0.26033287417603168), (+1.6918141611620747, +0.43723777783588935), (+1.0590096128247919, +0.94792444624606131), (+1.3059082775785895, +0.10109002262639510), (+1.0115745251812469, +0.93864712579456600), (+1.6714346113740954, +0.64501354562561386), (+1.3024215419037328, +0.46965306958282327), (+1.6654566750179582, +0.17272972444563839), (+1.5138346668187272, +0.31021851981293569), (+1.7223131788023847, +0.39764391776502828), (+1.1744170351890064, +0.31725410917744512), (+1.8732047696127458, +0.71202582821468685), (+1.9495453041134780, +0.76792889938007181), (+1.6159767177257849, +0.85339711034051569), (+1.2003066553499830, +0.55014626419226442), (+1.4723578486821423, +0.64504479567368678), (+1.7084582646030526, +0.10409896429086962), (+1.2989800090661627, +0.56497155293143941), (+1.7260174756412052, +0.64969081512347737), (+1.7161980085238953, +0.49903992484222615E-2), (+1.8696118809559552, +0.99504864716410923), (+1.3548553470729310, +0.42644811531940163), (+1.8600946357195260, +0.30025198413860654), (+1.1742192143077266, +0.83246473603524218), (+1.2964361818401327, +0.32996941911931377), (+1.8615548707010474, +0.50207337667474627), (+1.5978807852536936, +0.84181775677311999), (+1.9077610417656876, +0.80326852075292476), (+1.4578615105186663, +0.15718720944949349), (+1.2963650946725818, +0.87129518683542506), (+1.1376591061478694, +0.30518142779992896), (+1.5566338549829926, +0.34985093960375391), (+1.5903271662727216, +0.74757524393533015), (+1.0167917122237191, +0.39146306673241982), (+1.1865051522781933, +0.37377397222348052), (+1.1451410376108324, +0.29047310291773998), (+1.1946230943818819, +0.28119881606028296), (+1.7237140868997454, +0.15244525504491657), (+1.6814006188784425, +0.25878348023078757), (+1.6496617888089873, +0.33302904836438241), (+1.5321523686612939, +0.12806239695205324), (+1.4788020668406929, +0.43363727200899282), (+1.4705593020320480, +0.37642735005434502), (+1.9303784114581002, +0.67784777732615231), (+1.3462312254922610, +0.50819397861566706), (+1.0173862510015694, +0.40338480062205395), (+1.6910366178021405, +0.96929327824269451), (+1.1229952818683759, +0.71628126960008121), (+1.6324876750542971, +0.57131160667610292), (+1.7836380993046062, +0.35335860760364723)

330

331adat = getFFTR(getFFTF(data)) / size(data)

332adat

333(+1.5019857032984387, +0.16111036825601971), (+1.6775075177677063, +0.41271279713563834E-1), (+1.9618042815197960, +0.31163576728909897), (+1.4409941035752243, +0.39632393435528018), (+1.5755553898187953, +0.63793967660307149), (+1.9665943186874251, +0.66632024538881007), (+1.1670264656403531, +0.14002137980123451E-1), (+1.1069109991260790, +0.89985074088651718), (+1.4642076358035416, +0.91947586258458269), (+1.7017292514076041, +0.67221523467457445), (+1.3505446357193929, +0.42880065392576028), (+1.4371100993605936, +0.38511587248515250), (+1.1578045843773583, +0.72372456547642738), (+1.4788391260496598, +0.94360172756093375), (+1.5424460738138521, +0.26027516969416148), (+1.7178303591160324, +0.35458561555591428), (+1.8484004640711902, +0.75018149884742291), (+1.5277313612534289, +0.55425916813761622), (+1.9760780654156200, +0.29977926314061248), (+1.4195758020148475, +0.80822761531820841), (+1.6914324273071293, +0.66100322643336011E-2), (+1.3145766495964590, +0.95728320337143857), (+1.6010685111354490, +0.29365023958192676), (+1.5097994019176926, +0.72284328411660470), (+1.2566451641223124, +0.72327404776017457), (+1.3472625283165760, +0.30499860449770133), (+1.3790177514292472, +0.44825426609542474), (+1.7523640460057741, +0.31841678446966065), (+1.5703844984760198, +0.52548045206495297), (+1.2032223559783748, +0.91782294413784515), (+1.1501950288022353, +0.72923829983788668), (+1.0631420516962899, +0.83317916240009893), (+1.8506533938305074, +0.33238828995918696), (+1.1475260886419005, +0.60369042504404002), (+1.7121114223625518, +0.71934875374421015), (+1.5857316757481874, +0.93257131150376282), (+1.3247907132350729, +0.37363624880374546), (+1.1675367036342197, +0.72640128474529675), (+1.2618306207230292, +0.38754828431025912), (+1.9103591032597926, +0.30667162512795426), (+1.0693249001488752, +0.10747628570787740), (+1.9230469795395997, +0.61790567238822758), (+1.0020414401212310, +0.52188190419192293), (+1.1556931588920978, +0.12280152321092615), (+1.3988328270983803, +0.50228216478500905E-1), (+1.0916756877968361, +0.20793359400863909), (+1.8669092829224123, +0.95936422675018262), (+1.0931100155610951, +0.93167518897909329), (+1.9293689565237975, +0.15507290821847980), (+1.0538731948594258, +0.58085968604167060), (+1.7111899070897090, +0.26033287417603196), (+1.6918141611620752, +0.43723777783588941), (+1.0590096128247921, +0.94792444624606143), (+1.3059082775785904, +0.10109002262639515), (+1.0115745251812474, +0.93864712579456577), (+1.6714346113740961, +0.64501354562561408), (+1.3024215419037326, +0.46965306958282310), (+1.6654566750179589, +0.17272972444563822), (+1.5138346668187270, +0.31021851981293552), (+1.7223131788023847, +0.39764391776502833), (+1.1744170351890069, +0.31725410917744512), (+1.8732047696127463, +0.71202582821468663), (+1.9495453041134778, +0.76792889938007192), (+1.6159767177257849, +0.85339711034051580), (+1.2003066553499828, +0.55014626419226431), (+1.4723578486821429, +0.64504479567368700), (+1.7084582646030524, +0.10409896429086934), (+1.2989800090661625, +0.56497155293143941), (+1.7260174756412050, +0.64969081512347737), (+1.7161980085238955, +0.49903992484221860E-2), (+1.8696118809559550, +0.99504864716410935), (+1.3548553470729314, +0.42644811531940152), (+1.8600946357195260, +0.30025198413860649), (+1.1742192143077268, +0.83246473603524207), (+1.2964361818401324, +0.32996941911931371), (+1.8615548707010483, +0.50207337667474672), (+1.5978807852536940, +0.84181775677312021), (+1.9077610417656883, +0.80326852075292476), (+1.4578615105186665, +0.15718720944949338), (+1.2963650946725824, +0.87129518683542528), (+1.1376591061478700, +0.30518142779992902), (+1.5566338549829930, +0.34985093960375369), (+1.5903271662727212, +0.74757524393532993), (+1.0167917122237189, +0.39146306673241965), (+1.1865051522781935, +0.37377397222348047), (+1.1451410376108331, +0.29047310291774003), (+1.1946230943818821, +0.28119881606028285), (+1.7237140868997451, +0.15244525504491654), (+1.6814006188784427, +0.25878348023078745), (+1.6496617888089871, +0.33302904836438224), (+1.5321523686612941, +0.12806239695205335), (+1.4788020668406929, +0.43363727200899277), (+1.4705593020320475, +0.37642735005434502), (+1.9303784114581004, +0.67784777732615220), (+1.3462312254922608, +0.50819397861566695), (+1.0173862510015703, +0.40338480062205390), (+1.6910366178021405, +0.96929327824269451), (+1.1229952818683762, +0.71628126960008087), (+1.6324876750542969, +0.57131160667610303), (+1.7836380993046062, +0.35335860760364723)

334reltol = sqrt(epsilon(1._TKG))

335reltol

336+0.14901161193847656E-7

337isClose(data, adat, reltol = reltol)

338T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, adat, reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+61

344data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

345data

346(+1.28639611840326643837990700889045534, +0.326658653752040221749095905450671432E-1), (+1.35466084367173246950600426618777408, +0.218599151864059150820576033485414959), (+1.82416622737281351473437780682985116, +0.247177189668731127556486669603553414), (+1.01323496744352712375367057958397826, +0.157285909959967189679359856363521648), (+1.48313211931966110572882069090961902, +0.583503008177777758026750154838199449), (+1.61159042967481496669287446040503571, +0.817498992685958027405271399508868154), (+1.01573291049821096833577268430243869, +0.863322298296980510882474274082263807), (+1.38119798101229493365871110557559070, +0.272825719825458028571221397690163438), (+1.98012675695107733904136305935702266, +0.332790728193580412702661143713506173), (+1.45012083890714111458343918413714559, +0.683175734861025487969686547063487335E-1), (+1.77201993536518117164747785315023608, +0.962409462801752755897216811719282799), (+1.13085884340561784350788246010714925, +0.973508635040839915167394196772602103), (+1.34938037035144455477184317524418594, +0.396656683998319313409593948747591097), (+1.26691158271640419442544379807993995, +0.974710892531014094650201247044956017), (+1.48667910334651324020173030378743020, +0.833438703045961024578364237550902138), (+1.21975018928168789851646179616731407, +0.834713356693202948261905062550534313), (+1.48514384267525754953608211025660136, +0.460113337014347259291671953981801108), (+1.78307091531226015707114512051608247, +0.885886970501841800259383518254975048), (+1.68981678109092886937424823896461366, +0.353727797468489389151300813028098280), (+1.93355364759047296607201396210449901, +0.393889437807489765352577379593791099), (+1.58081700612142333432526339408732402, +0.771890450799894867505060560439621024), (+1.85817649776680685554124636868187971, +0.803984315969042770346144302653626301), (+1.16575484327881030872515150744781595, +0.245153293965987631376767699410921934), (+1.94605814341801259825638190694903437, +0.858332202453504038091966246439276272), (+1.34938919739913879625284369086153426, +0.157787819459009210899363574126108645E-1), (+1.55571461748452749143344656516706307, +0.385951720343452148797119595931168552), (+1.30637989753343036273604887186403479, +0.322216002465250991312707598134167473), (+1.92218031168728549360763423552826260, +0.346101552421214396242523357073145269), (+1.09011574991737486505956983803746158, +0.461005010155673302008829892787899341), (+1.91771912669032020378796644082089233, +0.378934720746344701537119078090740999), (+1.85148365755524620717231520417806988, +0.272968281938768148329230633049896333E-1), (+1.51939634499378046661403496165937733, +0.491795244574897064940214195242367257), (+1.90889250911377622899298641969841149, +0.616506323840110695370500663717579101), (+1.46000360948479824189017339896779305, +0.725888240226702576041940346927797127), (+1.30685679197221398645688310704889997, +0.173706087696622542681775603079378258), (+1.57568976531678402070718246759926188, +0.227169715542153711887467208886401864), (+1.42167360505577846528982662966950564, +0.285647070369140924473526927101217993), (+1.37389747910820928934460143868378309, +0.333735378828509719637046569679470224), (+1.66921846607206117285435655046510607, +0.134588785876876787914548910868885379), (+1.34109086997036774119732824638342354, +0.225466468612507806435832956414332087), (+1.31009896512131402354052843490247902, +0.186777317011302143552254863871607542), (+1.14423209798324885997597203084762301, +0.854210265812827678048219205987309173), (+1.63560017957421690186852022394830177, +0.774992012092939727325956459196557681), (+1.74471345861287465103729679099134030, +0.367283016590997641962980962310753104), (+1.37954701399415675841430885867949648, +0.397011171570431158236133801684715603), (+1.86476790135248544478422312000274568, +0.824824525187893986545886789345391966), (+1.61274070215336624630393358824865142, +0.544677078054074606053086075137853615E-1), (+1.03681426664926145896304918812680318, +0.737321008475908070590341485642457672), (+1.87275597882489049216946510212055044, +0.556740626869088198582436491769476962), (+1.25260417424036343947784135612401232, +0.393796365336639821031719301820140514), (+1.98709370485742932859710390742966227, +0.216547886359609515062213954583545499), (+1.39234751790397938948823218820732123, +0.162873754053924729652647091033418951), (+1.89401742665055928802322277499986844, +0.842955096145155114447843718097068658), (+1.15798164195066544144838826020139969, +0.981695212833826311053085992373552980), (+1.26282613610005613872423600418145964, +0.349832553789335885365567682238603055), (+1.06028085992533369606663797459462357, +0.293106962350194308400326049162108343), (+1.45577559339382449813299012243132007, +0.570441020535030743445217031448411133), (+1.71405672200445497321001111169619981, +0.610629045334301061873467295959481415), (+1.81298378167638199467378725396132910, +0.656914617741922852197006895148099329), (+1.32552983500164385324233449486801483, +0.672228378950603036973108282763672184), (+1.33443244769360759976395040232277344, +0.232882037337180244863819629943469077)

347

348adat = getFFTR(getFFTF(data)) / size(data)

349adat

350(+1.28639611840326643837990700889045669, +0.326658653752040221749095905450675284E-1), (+1.35466084367173246950600426618777428, +0.218599151864059150820576033485415104), (+1.82416622737281351473437780682985154, +0.247177189668731127556486669603553607), (+1.01323496744352712375367057958397807, +0.157285909959967189679359856363521696), (+1.48313211931966110572882069090961921, +0.583503008177777758026750154838199352), (+1.61159042967481496669287446040503610, +0.817498992685958027405271399508868154), (+1.01573291049821096833577268430243889, +0.863322298296980510882474274082263711), (+1.38119798101229493365871110557559128, +0.272825719825458028571221397690163631), (+1.98012675695107733904136305935702324, +0.332790728193580412702661143713506028), (+1.45012083890714111458343918413714597, +0.683175734861025487969686547063488779E-1), (+1.77201993536518117164747785315023608, +0.962409462801752755897216811719282799), (+1.13085884340561784350788246010714906, +0.973508635040839915167394196772601815), (+1.34938037035144455477184317524418671, +0.396656683998319313409593948747591482), (+1.26691158271640419442544379807993976, +0.974710892531014094650201247044956210), (+1.48667910334651324020173030378743001, +0.833438703045961024578364237550902331), (+1.21975018928168789851646179616731407, +0.834713356693202948261905062550534313), (+1.48514384267525754953608211025660136, +0.460113337014347259291671953981801156), (+1.78307091531226015707114512051608266, +0.885886970501841800259383518254975048), (+1.68981678109092886937424823896461385, +0.353727797468489389151300813028098376), (+1.93355364759047296607201396210449882, +0.393889437807489765352577379593791147), (+1.58081700612142333432526339408732421, +0.771890450799894867505060560439621120), (+1.85817649776680685554124636868187951, +0.803984315969042770346144302653626301), (+1.16575484327881030872515150744781672, +0.245153293965987631376767699410921886), (+1.94605814341801259825638190694903475, +0.858332202453504038091966246439276272), (+1.34938919739913879625284369086153484, +0.157787819459009210899363574126110450E-1), (+1.55571461748452749143344656516706384, +0.385951720343452148797119595931168552), (+1.30637989753343036273604887186403556, +0.322216002465250991312707598134167522), (+1.92218031168728549360763423552826337, +0.346101552421214396242523357073145461), (+1.09011574991737486505956983803746177, +0.461005010155673302008829892787899293), (+1.91771912669032020378796644082089233, +0.378934720746344701537119078090740807), (+1.85148365755524620717231520417807046, +0.272968281938768148329230633049895640E-1), (+1.51939634499378046661403496165937771, +0.491795244574897064940214195242367353), (+1.90889250911377622899298641969841130, +0.616506323840110695370500663717578812), (+1.46000360948479824189017339896779305, +0.725888240226702576041940346927797030), (+1.30685679197221398645688310704890074, +0.173706087696622542681775603079378307), (+1.57568976531678402070718246759926246, +0.227169715542153711887467208886401791), (+1.42167360505577846528982662966950679, +0.285647070369140924473526927101217993), (+1.37389747910820928934460143868378386, +0.333735378828509719637046569679470561), (+1.66921846607206117285435655046510646, +0.134588785876876787914548910868885090), (+1.34109086997036774119732824638342411, +0.225466468612507806435832956414332039), (+1.31009896512131402354052843490247902, +0.186777317011302143552254863871607470), (+1.14423209798324885997597203084762320, +0.854210265812827678048219205987309365), (+1.63560017957421690186852022394830158, +0.774992012092939727325956459196557488), (+1.74471345861287465103729679099134049, +0.367283016590997641962980962310753008), (+1.37954701399415675841430885867949686, +0.397011171570431158236133801684715506), (+1.86476790135248544478422312000274568, +0.824824525187893986545886789345392062), (+1.61274070215336624630393358824865161, +0.544677078054074606053086075137852713E-1), (+1.03681426664926145896304918812680318, +0.737321008475908070590341485642457768), (+1.87275597882489049216946510212055024, +0.556740626869088198582436491769477155), (+1.25260417424036343947784135612401289, +0.393796365336639821031719301820140851), (+1.98709370485742932859710390742966207, +0.216547886359609515062213954583545427), (+1.39234751790397938948823218820732104, +0.162873754053924729652647091033418759), (+1.89401742665055928802322277499986901, +0.842955096145155114447843718097068947), (+1.15798164195066544144838826020140008, +0.981695212833826311053085992373552788), (+1.26282613610005613872423600418145984, +0.349832553789335885365567682238603152), (+1.06028085992533369606663797459462357, +0.293106962350194308400326049162108295), (+1.45577559339382449813299012243132026, +0.570441020535030743445217031448411133), (+1.71405672200445497321001111169619981, +0.610629045334301061873467295959481415), (+1.81298378167638199467378725396132871, +0.656914617741922852197006895148099425), (+1.32552983500164385324233449486801503, +0.672228378950603036973108282763672088), (+1.33443244769360759976395040232277402, +0.232882037337180244863819629943469053)

351reltol = sqrt(epsilon(1._TKG))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, adat, reltol = reltol)

355T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

356call setAsserted(all(isClose(data, adat, reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+5

361data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

362data

363+1.27208364, +1.90015960, +1.23741364, +1.27116776, +1.14649212

364

365adat = getFFTR(getFFTF(data)) / size(data)

366adat

367+1.27208352, +1.90015960, +1.23741376, +1.27116799, +1.14649224

368reltol = sqrt(epsilon(1._TKG))

369reltol

370+0.345266977E-3

371isClose(data, adat, reltol = reltol)

372T, T, T, T, T

373call setAsserted(all(isClose(data, adat, reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+66

378data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

379data

380+1.5566707445155059, +1.6824131191868692, +1.0342271173558051, +1.4273699830924378, +1.3136428718856048, +1.0048169071328807, +1.6683975903631076, +1.8629040022020322, +1.9467888894721890, +1.5048267967318496, +1.1972208669812752, +1.0846549281357976, +1.6211021485228347, +1.6509184814545199, +1.2241650389535053, +1.6045630905499795, +1.8830521328850844, +1.7938976516477654, +1.8353876106177869, +1.5348756785582423, +1.3600858036646870, +1.6824789154816926, +1.8216981083671531, +1.6991096592178041, +1.7273945796537551, +1.8375796883957012, +1.6058272773561142, +1.7080142700043979, +1.9586518812871856, +1.2769492606768340, +1.5178705284435334, +1.6695116504785399, +1.5484778329617317, +1.4014005315447640, +1.3551440101089223, +1.6904742991535295, +1.6472329545281772, +1.2870063959112938, +1.0600241020307193, +1.3183548299423058, +1.4565023768117193, +1.1701036677257508, +1.9451831789343141, +1.4818040346188202, +1.4815339415584197, +1.0968594017747417, +1.1181222462209219, +1.6173186718087078, +1.4461831280559547, +1.5936021591298739, +1.5211323146900972, +1.2085722279937494, +1.5560188594771434, +1.9283898174125964, +1.3574471065460165, +1.5381596673136340, +1.2598832378868203, +1.1671973334092625, +1.5813907414585295, +1.1626187760590900, +1.7542356865518074, +1.6344239297853296, +1.5018427314585936, +1.0490451618429728, +1.7189042826675851, +1.1405718592928347

381

382adat = getFFTR(getFFTF(data)) / size(data)

383adat

384+1.5566707445155061, +1.6824131191868696, +1.0342271173558057, +1.4273699830924382, +1.3136428718856052, +1.0048169071328810, +1.6683975903631072, +1.8629040022020320, +1.9467888894721885, +1.5048267967318494, +1.1972208669812754, +1.0846549281357978, +1.6211021485228350, +1.6509184814545197, +1.2241650389535055, +1.6045630905499795, +1.8830521328850844, +1.7938976516477649, +1.8353876106177869, +1.5348756785582423, +1.3600858036646870, +1.6824789154816919, +1.8216981083671533, +1.6991096592178039, +1.7273945796537551, +1.8375796883957012, +1.6058272773561146, +1.7080142700043977, +1.9586518812871858, +1.2769492606768342, +1.5178705284435328, +1.6695116504785392, +1.5484778329617315, +1.4014005315447629, +1.3551440101089223, +1.6904742991535284, +1.6472329545281765, +1.2870063959112932, +1.0600241020307191, +1.3183548299423047, +1.4565023768117191, +1.1701036677257501, +1.9451831789343141, +1.4818040346188204, +1.4815339415584201, +1.0968594017747417, +1.1181222462209228, +1.6173186718087076, +1.4461831280559545, +1.5936021591298739, +1.5211323146900970, +1.2085722279937492, +1.5560188594771434, +1.9283898174125962, +1.3574471065460165, +1.5381596673136337, +1.2598832378868208, +1.1671973334092627, +1.5813907414585298, +1.1626187760590900, +1.7542356865518069, +1.6344239297853294, +1.5018427314585934, +1.0490451618429726, +1.7189042826675851, +1.1405718592928347

385reltol = sqrt(epsilon(1._TKG))

386reltol

387+0.14901161193847656E-7

388isClose(data, adat, reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, adat, reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+60

395data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

396data

397+1.49868442555478691783161592431286568, +1.48339313721584922477679810011691497, +1.03066899535065171064058267766293918, +1.30703395218898950519876192894478186, +1.34174895861939671499226885635172525, +1.89932040459586804488995921689388085, +1.93314867538090195108129900069324780, +1.25441523792444512645859600928406616, +1.30609310610237938812592154576975737, +1.59874325683491538481526354422249207, +1.99840921029528688304611768710379018, +1.91608940757430450825742053684610003, +1.16630316687149437912873691586487467, +1.80402821699531194583552363111332234, +1.63710850015212861068171386355769594, +1.60426787817487781179685384479852739, +1.98974767456798277015183123501617747, +1.28327980458590018533150632860913842, +1.11941003733177340312033495577690004, +1.07508035117320972609756847338338533, +1.65907874083848149771357055591849391, +1.35512736276696655161251657094796929, +1.57861580296469922885907502470834546, +1.21818530732986738576102144863471879, +1.06961529148000224618908036005648734, +1.40028096902004721579991116473877299, +1.54770671325414006486079890497376754, +1.54859633640312140423805627161469364, +1.04705045220293925498447613288624157, +1.10999875769553542046420397915854444, +1.41085776228352280514246159140034466, +1.17865832335647959803660465931346021, +1.53583491678776200716351394026571304, +1.01895605386241652286860912878272255, +1.68070363140923183454804516808216203, +1.94399870239126877102354217988962157, +1.22426786338296491699797218266922072, +1.65900305618168148887449176712792669, +1.91293007911362937190325330413357675, +1.68267353783796324433820195289584947, +1.05647495374085196281300044906105946, +1.48949628777268540358431027454523080, +1.78437600287331794388778769651753158, +1.00145959680914494490100728513181879, +1.11968430841570098239004711632744557, +1.96912714134502623052489222808934303, +1.81261960228821992241461125531898401, +1.54964574353648154341439054061038833, +1.44281516518315716082375298697173303, +1.71567667294165454385394680481355053, +1.20204855397073051416262588112544805, +1.26348386920594162088210983608118040, +1.98948760150957535093394126389770563, +1.46330605589553858288020417015763723, +1.58848909373278222343016124955469772, +1.87510707454348206343484318918581930, +1.97466547296284374412478597528812931, +1.34366445055878324429056233278008954, +1.41273845526089896442490096806571303, +1.12895222812556505575708354423964227

398

399adat = getFFTR(getFFTF(data)) / size(data)

400adat

401+1.49868442555478691783161592431286568, +1.48339313721584922477679810011691517, +1.03066899535065171064058267766293918, +1.30703395218898950519876192894478205, +1.34174895861939671499226885635172525, +1.89932040459586804488995921689388065, +1.93314867538090195108129900069324780, +1.25441523792444512645859600928406597, +1.30609310610237938812592154576975775, +1.59874325683491538481526354422249187, +1.99840921029528688304611768710379018, +1.91608940757430450825742053684610003, +1.16630316687149437912873691586487467, +1.80402821699531194583552363111332215, +1.63710850015212861068171386355769632, +1.60426787817487781179685384479852758, +1.98974767456798277015183123501617767, +1.28327980458590018533150632860913842, +1.11941003733177340312033495577690024, +1.07508035117320972609756847338338552, +1.65907874083848149771357055591849410, +1.35512736276696655161251657094796910, +1.57861580296469922885907502470834565, +1.21818530732986738576102144863471898, +1.06961529148000224618908036005648734, +1.40028096902004721579991116473877299, +1.54770671325414006486079890497376792, +1.54859633640312140423805627161469364, +1.04705045220293925498447613288624177, +1.10999875769553542046420397915854464, +1.41085776228352280514246159140034466, +1.17865832335647959803660465931346021, +1.53583491678776200716351394026571285, +1.01895605386241652286860912878272274, +1.68070363140923183454804516808216223, +1.94399870239126877102354217988962176, +1.22426786338296491699797218266922091, +1.65900305618168148887449176712792669, +1.91293007911362937190325330413357694, +1.68267353783796324433820195289584947, +1.05647495374085196281300044906105965, +1.48949628777268540358431027454523061, +1.78437600287331794388778769651753177, +1.00145959680914494490100728513181879, +1.11968430841570098239004711632744557, +1.96912714134502623052489222808934284, +1.81261960228821992241461125531898420, +1.54964574353648154341439054061038852, +1.44281516518315716082375298697173322, +1.71567667294165454385394680481355015, +1.20204855397073051416262588112544824, +1.26348386920594162088210983608118059, +1.98948760150957535093394126389770582, +1.46330605589553858288020417015763723, +1.58848909373278222343016124955469791, +1.87510707454348206343484318918581930, +1.97466547296284374412478597528812950, +1.34366445055878324429056233278008954, +1.41273845526089896442490096806571303, +1.12895222812556505575708354423964227

402reltol = sqrt(epsilon(1._TKG))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, adat, reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, adat, reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+39

412data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

413data

414(+1.01353979, +0.484881580), (+1.78222084, +0.716682076E-1), (+1.28242862, +0.745402634), (+1.88433123, +0.278641164), (+1.13915324, +0.333079100E-1), (+1.10978913, +0.883721888), (+1.21253681, +0.362086594), (+1.10299850, +0.118565321), (+1.40548766, +0.739075601), (+1.43066835, +0.241026163), (+1.95704544, +0.100190401), (+1.48804140, +0.772507250), (+1.42412424, +0.673407733), (+1.20349860, +0.244080245), (+1.60620403, +0.197491944), (+1.26902127, +0.485102713), (+1.52734697, +0.529820323), (+1.44439220, +0.441247582), (+1.00282741, +0.559205592), (+1.83250809, +0.666058362), (+1.98651838, +0.650457025), (+1.34398699, +0.315029562), (+1.93566680, +0.844424069), (+1.92721343, +0.659968436), (+1.98072433, +0.229674816), (+1.34257460, +0.590938628), (+1.30908394, +0.399637222E-2), (+1.07861447, +0.984243572), (+1.61966300, +0.794977546E-1), (+1.67058480, +0.659346879), (+1.52789187, +0.595845580), (+1.81186914, +0.108512342), (+1.69462872, +0.974396706), (+1.82788348, +0.790639222), (+1.24318123, +0.819378495), (+1.35135078, +0.139037251), (+1.08629966, +0.998049378), (+1.29352498, +0.540553927E-1), (+1.94673312, +0.616498590)

415

416adat = getFFTR(getFFTF(data)) / size(data)

417adat

418(+1.01353943, +0.484881520), (+1.78222072, +0.716681331E-1), (+1.28242850, +0.745402634), (+1.88433135, +0.278641164), (+1.13915300, +0.333077535E-1), (+1.10978913, +0.883721650), (+1.21253717, +0.362086594), (+1.10299885, +0.118565291), (+1.40548754, +0.739075661), (+1.43066823, +0.241026163), (+1.95704532, +0.100190312), (+1.48804116, +0.772507310), (+1.42412388, +0.673407793), (+1.20349836, +0.244080171), (+1.60620379, +0.197491914), (+1.26902139, +0.485102624), (+1.52734709, +0.529820383), (+1.44439232, +0.441247493), (+1.00282717, +0.559205413), (+1.83250856, +0.666058421), (+1.98651886, +0.650457203), (+1.34398675, +0.315029383), (+1.93566656, +0.844424009), (+1.92721379, +0.659968495), (+1.98072445, +0.229674786), (+1.34257424, +0.590938687), (+1.30908382, +0.399631122E-2), (+1.07861412, +0.984243453), (+1.61966288, +0.794977546E-1), (+1.67058504, +0.659346879), (+1.52789176, +0.595845640), (+1.81186891, +0.108512267), (+1.69462919, +0.974396706), (+1.82788384, +0.790639341), (+1.24318123, +0.819378376), (+1.35135055, +0.139037237), (+1.08629978, +0.998049438), (+1.29352486, +0.540553294E-1), (+1.94673288, +0.616498590)

419reltol = sqrt(epsilon(1._TKG))

420reltol

421+0.345266977E-3

422isClose(data, adat, reltol = reltol)

423T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, adat, reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+22

429data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

430data

431(+1.6657803849934010, +0.79051172805265224), (+1.1750450676306206, +0.99020725313648916E-1), (+1.5420950280655201, +0.61875384037479286), (+1.1405562709780730, +0.39703910320438374), (+1.7919260847795018, +0.97562379903813889E-1), (+1.5045885408010213, +0.48860997965107400), (+1.0627600553269834, +0.48819770566951326), (+1.1072119828071836, +0.89453018602127399E-1), (+1.8150065794647838, +0.84362483713919489), (+1.7214973489458050, +0.28309721456199188), (+1.6185223311603707, +0.61501603000876559), (+1.9896008498061004, +0.98838596543978086E-1), (+1.1652007359215730, +0.52386183832345157), (+1.2690989169572380, +0.10075471216487486), (+1.8401699824111095, +0.12702893827440909), (+1.1048760010258278, +0.13363043771471006), (+1.3099881312363517, +0.93353242620950172), (+1.1538310329846171, +0.49203596606678479), (+1.3706486084729310, +0.12316758066707012), (+1.8856942997484631, +0.81553419222689250), (+1.6082269067648713, +0.55595231650680743), (+1.5274066485406419, +0.33628814691266773)

432

433adat = getFFTR(getFFTF(data)) / size(data)

434adat

435(+1.6657803849934008, +0.79051172805265224), (+1.1750450676306208, +0.99020725313648861E-1), (+1.5420950280655203, +0.61875384037479308), (+1.1405562709780730, +0.39703910320438351), (+1.7919260847795022, +0.97562379903813903E-1), (+1.5045885408010213, +0.48860997965107428), (+1.0627600553269831, +0.48819770566951315), (+1.1072119828071834, +0.89453018602127413E-1), (+1.8150065794647838, +0.84362483713919501), (+1.7214973489458052, +0.28309721456199183), (+1.6185223311603707, +0.61501603000876548), (+1.9896008498061006, +0.98838596543977877E-1), (+1.1652007359215732, +0.52386183832345146), (+1.2690989169572384, +0.10075471216487492), (+1.8401699824111093, +0.12702893827440914), (+1.1048760010258276, +0.13363043771471006), (+1.3099881312363515, +0.93353242620950172), (+1.1538310329846171, +0.49203596606678490), (+1.3706486084729312, +0.12316758066707018), (+1.8856942997484636, +0.81553419222689216), (+1.6082269067648716, +0.55595231650680765), (+1.5274066485406421, +0.33628814691266756)

436reltol = sqrt(epsilon(1._TKG))

437reltol

438+0.14901161193847656E-7

439isClose(data, adat, reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, adat, reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+80

446data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

447data

448(+1.61420505977327780131470996903446364, +0.875111146257775027497354689166550502), (+1.14305852581959133514006988468356153, +0.319703508053503046452179914934793976), (+1.50499858167370791179912992959876992, +0.542781938750592608018269576073178315), (+1.01128790159179293193550398241839645, +0.278334715480959805791670407034025991), (+1.18678095488925439727665692209424269, +0.234630495468745678910861418833741769), (+1.07587339285578220803215032035537629, +0.868758393280226525582003525200996231), (+1.59536956386690515845976880961419040, +0.477158410836829165965390603857025747), (+1.18486502573557847758540719798406883, +0.487304336624333766935033889883432093), (+1.25872419734413600110403219505896387, +0.777261374382670081203491914361469718), (+1.80851394249893697495139616579028108, +0.489567712366709836587844531190974545), (+1.44341975366385182021485369223938058, +0.729612242288078028674999937475734676), (+1.32326156895085025187925931107317134, +0.293104829631413133796122252960977084), (+1.74897564458642134335349372250051416, +0.904628200735088678880248991207244172), (+1.98124614874031879364242698666540877, +0.163177992100795641805028889458224973), (+1.04310007158686027805550184304674106, +0.786883549435408641015948082364539036), (+1.44140826437770125818118548299004147, +0.914213113095394245103955221660476831), (+1.52697755379426202680076146185285900, +0.411985274278671408061593739280779991), (+1.97773955733590711875056103744306886, +0.399633477879794601337590746761796809), (+1.89937359534596269438905445526458974, +0.516013786546830330256490592698025464), (+1.18760044776561655466413515620550028, +0.484982963971016003464187994673559936), (+1.74353772133063593735767166870072240, +0.784010101717821547334894170789338739), (+1.39758468703034195164707920627434180, +0.169176057540429053556199724173738466), (+1.52733392598279345737118413455303652, +0.676331280293204285055666616128510992), (+1.99132176032487967977843941722231345, +0.932253646357405735666505795718269570), (+1.15017451243987748279749110656559949, +0.839157845306931061611480384027772204), (+1.24513326537778119307492634400508703, +0.675328106884045929584089336913125021), (+1.99431390160091740587693265107011731, +0.961466251755960364798562475339186198), (+1.41933638648099920899599930023775653, +0.919481377338569926347502934338272477), (+1.81120848835679556837030017649275197, +0.891522376934351615604664985912670428), (+1.62964235083344860101800799782735459, +0.766384198889606210526916596130192986), (+1.42890101288894088608661189317242364, +0.849999949742008852730218303899467113), (+1.06597995325798831331687023850593389, +0.463310239545081825202948712614794617), (+1.89945176895068732681770005031110861, +0.782442366520827956187979462565535935E-1), (+1.41036294506482408372491915070949724, +0.228379490758403693897495059853075844), (+1.58202072153624837326704228042020392, +0.725279114816493051944465686027488978), (+1.07168387302186434971212227608183813, +0.327761822779446743769450762592672091), (+1.90819847806855282184160571528119440, +0.615766173872611311333138510277528190), (+1.84829446870895843036161077142364353, +0.688300423614417384201705560977135032), (+1.30592618996641364212958015601181707, +0.719412475078502915360308870299255268), (+1.50570366157335607138099253317579843, +0.403278637057683523553210095124749901), (+1.73590777030915212399826326567273597, +0.469278486665799031361514834871348231E-1), (+1.35848561320189940906487651922001559, +0.413633144015940534600361409111001856), (+1.19998790215929263601462178700936922, +0.802382079440300820791410725508117062), (+1.32631893234701839923146800273565095, +0.616832114177738958910478670811391824), (+1.70784114596879635713890036996731176, +0.707521506015800999116964585070597525E-1), (+1.05121585386238311169450278589445297, +0.429421556492962333773313731254334174), (+1.85710201820465261235491560603356105, +0.619142355329770815442126697047680695), (+1.01628473810164299065266535749817746, +0.100593836472781336155649488770261821), (+1.91117219082410920440281992595704606, +0.529125542247495863937656540084392943), (+1.31932548842939161030477184044554970, +0.793803109958416725904668089111741020), (+1.91157800356846574111729750538138031, +0.888901462842657306760567400680451255E-1), (+1.55103203230061353308071193868117015, +0.433905983233932939650197365742097531E-1), (+1.09745401232289735540231277843231455, +0.798155196918498249312527421823724265), (+1.63029563665373393597401757400543913, +0.666112029639270853896079650053469783), (+1.66957274527220968411713342343658322, +0.537785296480113196117482025744530190), (+1.32648108016168395045200130165283442, +0.978856797440956739410561986690946996), (+1.68747254303193161133709799484722697, +0.236217630881190518613450361394059344), (+1.08038458438928337737257626260023215, +0.798941376023065510004462225130767942), (+1.83182687338186583789520743377763519, +0.427901242656226141895914839281889132), (+1.73839807646111816851574024294584225, +0.513230624446891695162198829289171667), (+1.58014183654039598278557064571913685, +0.369803661420447219915909850134993205E-1), (+1.27409492370349737299235765586233002, +0.557836496643859154799464543606180573), (+1.48925600938506612720186292934046125, +0.409959846664830822131899123375924344), (+1.62834304642971340020177640953914790, +0.543309132710020546093154292456992688), (+1.07693205685557278266703690831529957, +0.814261927772885461240015737856889069E-1), (+1.73909912027658005242273370264062274, +0.687850716517049734635529887190510259), (+1.41351721011274601750849043317133095, +0.463359779375172910330344117269931446), (+1.31801087951784148575036418863300108, +0.528738745426756396002915763733567676), (+1.35447524172939655710532076477887923, +0.704817460950862640091044416693051206), (+1.91403725758409742323677932195938925, +0.483389020967666396081201620220082744), (+1.49012649315082788321007979377084054, +0.453956008286511765223365218591439734), (+1.45798016452184453282062294315838132, +0.555539035323645186073612859523165477), (+1.79017445225862434453096727192807237, +0.331118122502139915807183586049371159), (+1.33174521367774627768269468956316909, +0.978107787701992819774438988314031245), (+1.94109282640971746114271317219225092, +0.592799391045579202623785022374570704), (+1.00087640880795728690827538713319232, +0.336950387259782845329282796900224575), (+1.63818952925957141852597537712975340, +0.376964301763486001234511987858460383), (+1.19696606750008085534156985591828473, +0.327695524111199420792370399605206164), (+1.94480036020699708840982145103785945, +0.651604773265353953696828013020208931), (+1.14967305759704184017298807016836960, +0.340024114394869388325880645755645208)

449

450adat = getFFTR(getFFTF(data)) / size(data)

451adat

452(+1.61420505977327780131470996903446326, +0.875111146257775027497354689166550502), (+1.14305852581959133514006988468356172, +0.319703508053503046452179914934794072), (+1.50499858167370791179912992959877011, +0.542781938750592608018269576073178315), (+1.01128790159179293193550398241839645, +0.278334715480959805791670407034025942), (+1.18678095488925439727665692209424289, +0.234630495468745678910861418833741721), (+1.07587339285578220803215032035537629, +0.868758393280226525582003525200996423), (+1.59536956386690515845976880961419040, +0.477158410836829165965390603857025843), (+1.18486502573557847758540719798406883, +0.487304336624333766935033889883432238), (+1.25872419734413600110403219505896368, +0.777261374382670081203491914361469526), (+1.80851394249893697495139616579028089, +0.489567712366709836587844531190974545), (+1.44341975366385182021485369223938038, +0.729612242288078028674999937475734580), (+1.32326156895085025187925931107317134, +0.293104829631413133796122252960977084), (+1.74897564458642134335349372250051416, +0.904628200735088678880248991207244172), (+1.98124614874031879364242698666540877, +0.163177992100795641805028889458224925), (+1.04310007158686027805550184304674106, +0.786883549435408641015948082364539036), (+1.44140826437770125818118548299004109, +0.914213113095394245103955221660476831), (+1.52697755379426202680076146185285919, +0.411985274278671408061593739280779943), (+1.97773955733590711875056103744306867, +0.399633477879794601337590746761796953), (+1.89937359534596269438905445526458974, +0.516013786546830330256490592698025464), (+1.18760044776561655466413515620550047, +0.484982963971016003464187994673559887), (+1.74353772133063593735767166870072220, +0.784010101717821547334894170789338739), (+1.39758468703034195164707920627434180, +0.169176057540429053556199724173738514), (+1.52733392598279345737118413455303652, +0.676331280293204285055666616128510992), (+1.99132176032487967977843941722231306, +0.932253646357405735666505795718269570), (+1.15017451243987748279749110656559968, +0.839157845306931061611480384027772204), (+1.24513326537778119307492634400508684, +0.675328106884045929584089336913125021), (+1.99431390160091740587693265107011750, +0.961466251755960364798562475339186198), (+1.41933638648099920899599930023775614, +0.919481377338569926347502934338272574), (+1.81120848835679556837030017649275197, +0.891522376934351615604664985912670428), (+1.62964235083344860101800799782735459, +0.766384198889606210526916596130192986), (+1.42890101288894088608661189317242345, +0.849999949742008852730218303899467017), (+1.06597995325798831331687023850593389, +0.463310239545081825202948712614794617), (+1.89945176895068732681770005031110842, +0.782442366520827956187979462565534009E-1), (+1.41036294506482408372491915070949705, +0.228379490758403693897495059853075988), (+1.58202072153624837326704228042020430, +0.725279114816493051944465686027488786), (+1.07168387302186434971212227608183774, +0.327761822779446743769450762592672091), (+1.90819847806855282184160571528119421, +0.615766173872611311333138510277528190), (+1.84829446870895843036161077142364353, +0.688300423614417384201705560977135225), (+1.30592618996641364212958015601181707, +0.719412475078502915360308870299255365), (+1.50570366157335607138099253317579863, +0.403278637057683523553210095124749997), (+1.73590777030915212399826326567273578, +0.469278486665799031361514834871348352E-1), (+1.35848561320189940906487651922001540, +0.413633144015940534600361409111002000), (+1.19998790215929263601462178700936941, +0.802382079440300820791410725508116773), (+1.32631893234701839923146800273565114, +0.616832114177738958910478670811391824), (+1.70784114596879635713890036996731176, +0.707521506015800999116964585070597886E-1), (+1.05121585386238311169450278589445317, +0.429421556492962333773313731254334077), (+1.85710201820465261235491560603356144, +0.619142355329770815442126697047680695), (+1.01628473810164299065266535749817746, +0.100593836472781336155649488770261881), (+1.91117219082410920440281992595704587, +0.529125542247495863937656540084392847), (+1.31932548842939161030477184044554951, +0.793803109958416725904668089111741116), (+1.91157800356846574111729750538138050, +0.888901462842657306760567400680450532E-1), (+1.55103203230061353308071193868117015, +0.433905983233932939650197365742097531E-1), (+1.09745401232289735540231277843231455, +0.798155196918498249312527421823724457), (+1.63029563665373393597401757400543894, +0.666112029639270853896079650053469879), (+1.66957274527220968411713342343658322, +0.537785296480113196117482025744529997), (+1.32648108016168395045200130165283404, +0.978856797440956739410561986690946900), (+1.68747254303193161133709799484722677, +0.236217630881190518613450361394059296), (+1.08038458438928337737257626260023157, +0.798941376023065510004462225130768038), (+1.83182687338186583789520743377763519, +0.427901242656226141895914839281889083), (+1.73839807646111816851574024294584225, +0.513230624446891695162198829289171763), (+1.58014183654039598278557064571913685, +0.369803661420447219915909850134992242E-1), (+1.27409492370349737299235765586232983, +0.557836496643859154799464543606180669), (+1.48925600938506612720186292934046144, +0.409959846664830822131899123375924199), (+1.62834304642971340020177640953914771, +0.543309132710020546093154292456992784), (+1.07693205685557278266703690831529957, +0.814261927772885461240015737856888708E-1), (+1.73909912027658005242273370264062274, +0.687850716517049734635529887190510355), (+1.41351721011274601750849043317133114, +0.463359779375172910330344117269931349), (+1.31801087951784148575036418863300088, +0.528738745426756396002915763733567868), (+1.35447524172939655710532076477887904, +0.704817460950862640091044416693051206), (+1.91403725758409742323677932195938906, +0.483389020967666396081201620220082744), (+1.49012649315082788321007979377084034, +0.453956008286511765223365218591439782), (+1.45798016452184453282062294315838113, +0.555539035323645186073612859523165477), (+1.79017445225862434453096727192807218, +0.331118122502139915807183586049370967), (+1.33174521367774627768269468956316909, +0.978107787701992819774438988314031342), (+1.94109282640971746114271317219225111, +0.592799391045579202623785022374570704), (+1.00087640880795728690827538713319232, +0.336950387259782845329282796900224575), (+1.63818952925957141852597537712975359, +0.376964301763486001234511987858460335), (+1.19696606750008085534156985591828454, +0.327695524111199420792370399605206164), (+1.94480036020699708840982145103785945, +0.651604773265353953696828013020208835), (+1.14967305759704184017298807016836979, +0.340024114394869388325880645755645063)

453reltol = sqrt(epsilon(1._TKG))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, adat, reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, adat, reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+59

463data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

464data

465+1.61705351, +1.30184436, +1.90606952, +1.17068744, +1.51028156, +1.07776523, +1.50096416, +1.37883246, +1.04359221, +1.29617012, +1.84501457, +1.18625605, +1.88940001, +1.10689294, +1.00964642, +1.17566943, +1.46253324, +1.37207961, +1.29685974, +1.33631468, +1.11561787, +1.68625891, +1.88157368, +1.17391133, +1.70456481, +1.08171344, +1.66218805, +1.40890026, +1.47398758, +1.61228561, +1.56815386, +1.40587854, +1.26979506, +1.64653826, +1.39784431, +1.44926190, +1.92276382, +1.65808058, +1.29776669, +1.36289489, +1.63733530, +1.42045927, +1.01894712, +1.82074511, +1.62705386, +1.06613731, +1.72744679, +1.24353528, +1.77884841, +1.95075011, +1.94014335, +1.46886230, +1.77107000, +1.27793455, +1.12000537, +1.03429389, +1.73276711, +1.42314196, +1.42756474

466

467adat = getFFTR(getFFTF(data)) / size(data)

468adat

469+1.61705315, +1.30184376, +1.90606940, +1.17068636, +1.51028180, +1.07776439, +1.50096488, +1.37883282, +1.04359126, +1.29616821, +1.84501755, +1.18625319, +1.88940406, +1.10689104, +1.00964534, +1.17566872, +1.46253419, +1.37207949, +1.29685831, +1.33631492, +1.11561430, +1.68626046, +1.88157761, +1.17390490, +1.70457017, +1.08170748, +1.66219282, +1.40889978, +1.47398782, +1.61228907, +1.56815672, +1.40587878, +1.26979315, +1.64654171, +1.39784324, +1.44925988, +1.92276728, +1.65808129, +1.29776442, +1.36289310, +1.63733721, +1.42045915, +1.01894188, +1.82074881, +1.62705505, +1.06613386, +1.72745001, +1.24353182, +1.77884996, +1.95075059, +1.94014394, +1.46886098, +1.77107155, +1.27793372, +1.12000513, +1.03429270, +1.73276687, +1.42314136, +1.42756438

470reltol = sqrt(epsilon(1._TKG))

471reltol

472+0.345266977E-3

473isClose(data, adat, reltol = reltol)

474T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

475call setAsserted(all(isClose(data, adat, reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+16

480data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

481data

482+1.1817551712056313, +1.4397290115694825, +1.9052509768306169, +1.2649282244047324, +1.6700457348027160, +1.3184277410635572, +1.4370821532760023, +1.6040566193983650, +1.4551224393763755, +1.9190494341537387, +1.0261667882884975, +1.7479591453219823, +1.8375276566255256, +1.5410092471224632, +1.9727361876689331, +1.8610293717530522

483

484adat = getFFTR(getFFTF(data)) / size(data)

485adat

486+1.1817551712056311, +1.4397290115694821, +1.9052509768306169, +1.2649282244047322, +1.6700457348027160, +1.3184277410635572, +1.4370821532760025, +1.6040566193983645, +1.4551224393763753, +1.9190494341537385, +1.0261667882884975, +1.7479591453219820, +1.8375276566255256, +1.5410092471224630, +1.9727361876689333, +1.8610293717530517

487reltol = sqrt(epsilon(1._TKG))

488reltol

489+0.14901161193847656E-7

490isClose(data, adat, reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, adat, reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+9

497data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

498data

499+1.57048913274236206376362150152082780, +1.38505326506501020790552680296780745, +1.47048910837325609912460877349453203, +1.14757003463878569430490862478033847, +1.55560158600895436712097967904219230, +1.67655971006726576044574962906702600, +1.31885347654041431508379976365218773, +1.06992720732514517395506931795138431, +1.67317494184948564642696654734904221

500

501adat = getFFTR(getFFTF(data)) / size(data)

502adat

503+1.57048913274236206376362150152082761, +1.38505326506501020790552680296780764, +1.47048910837325609912460877349453222, +1.14757003463878569430490862478033828, +1.55560158600895436712097967904219249, +1.67655971006726576044574962906702620, +1.31885347654041431508379976365218754, +1.06992720732514517395506931795138470, +1.67317494184948564642696654734904240

504reltol = sqrt(epsilon(1._TKG))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, adat, reltol = reltol)

508T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, adat, reltol = reltol)))

510

511

Test:: test_pm_fftpack

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 1156 of file pm_fftpack.F90.

The documentation for this interface was generated from the following file:

src/fortran/main/pm_fftpack.F90